CRAFT: Cost-aware Refinement And Front-aware Tuning of Prompts

# CRAFT: Cost-aware Refinement And Front-aware Tuning of Prompts
Source: [https://arxiv.org/html/2606.04661](https://arxiv.org/html/2606.04661)
Shanu Kumar1, Shubhanshu Khandelwal2, Akhila Yesantarao Venkata2, Parag Agrawal2, Yova Kementchedjhieva1, Manish Gupta2 1MBZUAI2Microsoft \{shanu\.kumar,yova\.kementchedjhieva\}@mbzuai\.ac\.ae \{shukhand,akyesant,paragag,gmanish\}@microsoft\.com

###### Abstract

Prompts tuned for accuracy often grow long, raising inference cost on every model call\. The best accuracy\-cost trade\-off depends on the task and the budget, so prompt optimization is a search over the*Pareto front*of accuracy and prompt\-token cost rather than for one prompt\. The usual shortcut, collapsing the objectives into a weighted sum, fixes the trade\-off weight before search and often recovers only a narrow region of the front, a failure we call*scalarization collapse*\. We presentCRAFT\(Cost\-aware Refinement And Front\-aware Tuning\), a Pareto\-front prompt optimizer that treats target\-LLM validation calls as the scarce resource and allocates them to candidates near the optimistic candidate front\. Each round, complementary accuracy\-oriented and cost\-oriented generators propose edits, Pareto\-gap acquisition spends the per\-round validation budget, and NSGA\-II retention keeps a spread\-out population\. Across six classification and reasoning benchmarks, CRAFT’s retained fronts reach both high\-accuracy and low\-cost regions, while accuracy\-only, cost\-only, and weighted\-sum baselines each concentrate in narrower regions\. The accuracy\-cost trade\-off becomes a post\-search choice, not a pre\-search weight\.

CRAFT: Cost\-aware Refinement And Front\-aware Tuning of Prompts

Shanu Kumar1, Shubhanshu Khandelwal2, Akhila Yesantarao Venkata2,Parag Agrawal2, Yova Kementchedjhieva1, Manish Gupta21MBZUAI2Microsoft\{shanu\.kumar,yova\.kementchedjhieva\}@mbzuai\.ac\.ae\{shukhand,akyesant,paragag,gmanish\}@microsoft\.com

## 1Introduction

Large language models \(LLMs\) are adapted to downstream tasks by tuning the natural\-language prompt fed to the model\(Ramnathet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib263)\)\. Longer, more structured prompts cost more per call, and small edits change predictions disproportionately\(Jianget al\.,[2020](https://arxiv.org/html/2606.04661#bib.bib209); Zhaoet al\.,[2021](https://arxiv.org/html/2606.04661#bib.bib207)\), motivating automatic prompt optimization\.

Prior work splits along two paths\. Accuracy\-oriented optimizers, e\.g\., OPRO\(Yanget al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib9)\), ProTeGi\(Pryzantet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib15)\), SCULPT\(Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\), and EvoPrompt\(Guoet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib19)\), maximize task accuracy; prompt\-compression methods, e\.g\., Gist tokens\(Muet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib249)\), LLMLingua and LLMLingua\-2\(Jianget al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib236); Panet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib230)\), reduce token count to lower per\-call inference cost\(Chenet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib247)\)\. Both lines treat a prompt as good or bad along one axis, yet two prompts of similar accuracy but different lengths are not equivalent: each extra token adds to inference cost on every model call, so accuracy and cost are coupled\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x1.png)Figure 1:Accuracy\-cost trade\-off on BeaverTails\. SCULPT \(accuracy\-only\), LLMLingua \(cost\-only\), and WPRO0\.5\(weighted\-sum\) each collapse to a narrow region of the front\. CRAFT \(ours\) covers both high\-accuracy and low\-token regions of the front\.This creates a multi\-objective prompt\-optimization problem\. The objectives often conflict: higher accuracy tends to require more detailed prompts, while lower cost favors concise ones\. The relationship between prompt text and both accuracy and cost is non\-convex, and the prompt space is discrete\(Wenet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib6); Jianget al\.,[2020](https://arxiv.org/html/2606.04661#bib.bib209); Zhaoet al\.,[2021](https://arxiv.org/html/2606.04661#bib.bib207)\), so the trade\-off surface contains regions that a fixed scalar reward misses\(Das and Dennis,[1997](https://arxiv.org/html/2606.04661#bib.bib258)\)\. We instead optimize the accuracy\-cost Pareto front directly, defined as the set of prompts for which no other prompt is both more accurate and shorter\.

The algorithmic challenge is not merely choosing among evaluated trade\-offs, but deciding what to evaluate: each candidate’s accuracy requires target\-LLM validation calls, so the optimizer must spend a per\-round validation budget before the candidate’s true front position is known\. Optimizing a fixed scalar reward before search often recovers only a narrow region of the front, the*scalarization collapse*above\. We propose CRAFT \(Cost\-aware Refinement And Front\-aware Tuning\), a front\-aware optimization loop: the refiner and condenser generate edits with complementary accuracy and cost biases; Pareto\-gap acquisition\(Srinivaset al\.,[2009](https://arxiv.org/html/2606.04661#bib.bib245); Daultonet al\.,[2021](https://arxiv.org/html/2606.04661#bib.bib246)\)allocates the per\-round validation budget to candidates near the optimistic candidate front; and Non\-dominated Sorting Genetic Algorithm II \(NSGA\-II\) retention\(Debet al\.,[2002](https://arxiv.org/html/2606.04661#bib.bib240)\)keeps a diverse validated population for the next round\. Figure[1](https://arxiv.org/html/2606.04661#S1.F1)illustrates the contrast: accuracy\-only, cost\-only, and weighted\-sum baselines each concentrate on a narrow region of the front, while CRAFT covers both ends\.

Our contributions are: \(i\) we formalize cost\-aware prompt optimization as budgeted Pareto\-front search over accuracy and prompt\-token cost, where target\-LLM validation calls govern which candidate trade\-offs can be observed; \(ii\) we proposeCRAFT,111Code:[https://github\.com/Sshanu/CRAFT](https://github.com/Sshanu/CRAFT)a front\-aware framework that separates candidate generation from validation allocation, using complementary accuracy\-oriented and cost\-oriented generators, Pareto\-gap acquisition, and NSGA\-II retention as one budgeted loop; \(iii\) we show that accuracy\-only, cost\-only, and weighted\-sum baselines concentrate in narrow regions of the front, while CRAFT retains feasible prompts across high\-accuracy and low\-cost parts of the front on six benchmarks and transfers across optimizer LLMs\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x2.png)Figure 2:CRAFT framework\. Each round, the refiner and condenser generate new candidates from the previous population𝒫t−1\\mathcal\{P\}\_\{t\-1\}; Pareto\-gap acquisition validates them under the per\-round validation budget; the NSGA\-II selector retains a non\-dominated, spread\-out population𝒫t\\mathcal\{P\}\_\{t\}for the next round\. The loop repeats forRRrounds\.
## 2Related Work

##### Prompt Refinement\.

Prompt optimizers fall into four families, based on the optimization signal they use: \(1\) LLM\-edit methods rewrite prompts via another LLM\(Yanget al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib9); Pryzantet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib15); Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\), \(2\) gradient or program\-based methods that propagate signal through differentiable or symbolic graphs\(Yuksekgonulet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib21); Khattabet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib22)\), \(3\) RL\-based methods\(Denget al\.,[2022](https://arxiv.org/html/2606.04661#bib.bib235)\), and \(4\) evolutionary mutation\-and\-selection methods\(Guoet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib19); Fernandoet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib20)\)\. Most operate on raw text tokens, which makes large structural edits hard to express\. A small subset of refiners edit at the compile\-time or tree\-level abstraction\(Schnabel and Neville,[2024](https://arxiv.org/html/2606.04661#bib.bib23); Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\)\. CRAFT builds on this structure\-aware line, adopting SCULPT\(Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\)as its default refiner \(§[3\.2](https://arxiv.org/html/2606.04661#S3.SS2)\) for its accuracy\-oriented strength and treating it as swappable, with drop\-in replacements tested in Table[1](https://arxiv.org/html/2606.04661#S5.T1)\.

##### Prompt Compression\.

Token\-level compressors drop low\-information surface tokens to reduce length\(Muet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib249); Jianget al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib236); Panet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib230)\)\. Because they operate below the level of instructions or constraints, aggressive compression can remove task\-critical content; this limits their value as a cost\-oriented module inside a Pareto\-front loop\. A structure\-aware compressor that edits the parsed prompt tree could avoid this failure mode, but we are not aware of prior work in this direction; we introduce one \(DISTILL, §[3\.3](https://arxiv.org/html/2606.04661#S3.SS3)\) as CRAFT’s cost\-oriented generator\.

##### Multi\-Objective Prompt Optimization\.

Existing multi\-objective prompt optimizers\(Jafariet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib231); Menchaca Resendiz and Klinger,[2025](https://arxiv.org/html/2606.04661#bib.bib242); Zhaoet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib233); Yang and Li,[2023](https://arxiv.org/html/2606.04661#bib.bib232); Agrawalet al\.,[2026](https://arxiv.org/html/2606.04661#bib.bib243)\)optimize multi\-objective rewards, but they do not study front construction when each candidate’s accuracy must be estimated with target\-LLM validation calls and a fixed budget can cover only part of the discrete prompt set\. CRAFT targets that budgeted front\-construction setting for accuracy versus prompt\-token cost\. The closest cost\-aware optimizer is CAPO \(Cost\-Aware Prompt Optimization\)\(Zehleet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib261)\); we adapt its fixed\-weight scalarization as our WPRO baseline; the resulting scalarization collapse is shown in Figure[1](https://arxiv.org/html/2606.04661#S1.F1)\.

##### Multi\-Objective Bayesian Optimization and Cost\-Aware Inference\.

Multi\-objective Bayesian optimization\(Knowles,[2006](https://arxiv.org/html/2606.04661#bib.bib244); Srinivaset al\.,[2009](https://arxiv.org/html/2606.04661#bib.bib245); Daultonet al\.,[2021](https://arxiv.org/html/2606.04661#bib.bib246)\)frames our problem but assumes numerical design spaces and Gaussian\-process surrogates, neither available for discrete text; an acquisition rule on partial\-validation scores is needed instead\. Cost\-aware LLM inference\(Chenet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib247); Yueet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib248)\)routes inputs across models at inference time and is orthogonal to prompt optimization\.

## 3The CRAFT Framework

CRAFT maintains a small population of prompts and, round by round, reshapes it into an approximation of the accuracy\-cost Pareto front\. Each round has three steps: a structure\-aware refiner and condenser propose new candidates \(§[3\.2](https://arxiv.org/html/2606.04661#S3.SS2), §[3\.3](https://arxiv.org/html/2606.04661#S3.SS3)\); a Pareto\-gap acquisition function spends the per\-round validation budget on the candidates near the optimistic candidate front \(§[3\.4](https://arxiv.org/html/2606.04661#S3.SS4)\); and a population selector keepskkprompts spread across the front for the next round \(§[3\.5](https://arxiv.org/html/2606.04661#S3.SS5)\)\. Figure[2](https://arxiv.org/html/2606.04661#S1.F2)shows the loop\.

### 3\.1Problem Formulation

We cast prompt optimization as a bi\-objective search over a task\-accuracy score and a prompt\-token cost\. Let𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}and𝒟test\\mathcal\{D\}\_\{\\mathrm\{test\}\}be the validation and held\-out test sets, of sizesNvalN\_\{\\mathrm\{val\}\}andNtestN\_\{\\mathrm\{test\}\}\. For a promptPPand a subset𝒱⊆𝒟val\\mathcal\{V\}\\subseteq\\mathcal\{D\}\_\{\\mathrm\{val\}\},p​\(P;𝒱\)p\(P;\\mathcal\{V\}\)is the task score on𝒱\\mathcal\{V\}\. For a candidatePiP\_\{i\}we writepi=p​\(Pi;𝒟val\)p\_\{i\}=p\(P\_\{i\};\\mathcal\{D\}\_\{\\mathrm\{val\}\}\)for its full\-validation score \(the objective that search ultimately optimizes\), andci=c​\(Pi\)c\_\{i\}=c\(P\_\{i\}\)for its cost, the number of prompt tokens, excluding example inputs and model outputs\. During searchpip\_\{i\}is estimated from partial validation \(§[3\.4](https://arxiv.org/html/2606.04661#S3.SS4)\), while held\-out test scores are reserved for final reporting \(Appendix[B\.1](https://arxiv.org/html/2606.04661#A2.SS1)\)\. The two objectives are in tension, so no single prompt is uniformly best\. A promptPiP\_\{i\}*dominates*PjP\_\{j\}, writtenPi≻PjP\_\{i\}\\succ P\_\{j\}, if it is no worse on both objectives and strictly better on one:pi≥pjp\_\{i\}\\geq p\_\{j\}andci≤cjc\_\{i\}\\leq c\_\{j\}, with at least one strict inequality\. The prompts of a set𝒞\\mathcal\{C\}that no other prompt dominates form its*Pareto\-optimal set*𝒞∗\\mathcal\{C\}^\{\*\}, and CRAFT’s goal is to approximate𝒞∗\\mathcal\{C\}^\{\*\}over the discrete space of LLM prompts under a fixed budget of LLM calls per round\.

CRAFT builds this approximation iteratively, starting from a single hand\-written prompt\. Roundttopens with a retained population𝒫t−1\\mathcal\{P\}\_\{t\-1\}ofkkprompts\. The refiner and condenser expand it into a candidate set𝒬t\\mathcal\{Q\}\_\{t\}; the acquisition function validates a budgeted subset of𝒬t\\mathcal\{Q\}\_\{t\}; and the selector keepskkvalidated prompts as the next population𝒫t\\mathcal\{P\}\_\{t\}\. AfterRRrounds,𝒫R\\mathcal\{P\}\_\{R\}is the returned front approximation\.

### 3\.2Refiner

CRAFT draws candidates from two modules with opposite biases\. Optimizing accuracy alone inflates prompts; optimizing cost alone strips away task signal\. An accuracy\-oriented*refiner*\(this subsection\) targets higher task accuracy, and a cost\-oriented*condenser*\(§[3\.3](https://arxiv.org/html/2606.04661#S3.SS3)\) targets lower prompt\-token cost; keeping both in the population lets the selector trade the two off\. The refiner is any accuracy\-oriented prompt optimizer compatible with the per\-round budget interface; SCULPT, OPRO, and EvoPrompt are all interchangeable in this role\. We use SCULPT as the default for two reasons: prior work shows it generalizes across a broader set of benchmarks than OPRO\(Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\), and its tree\-level edits are precise and stable\. SCULPT’s critic\-actor scaffold \(Appendix[A\.3](https://arxiv.org/html/2606.04661#A1.SS3), Figure[8](https://arxiv.org/html/2606.04661#A1.F8)\) parses the prompt into a hierarchical tree of sections, rules, and examples; a critic\-actor pair edits that tree by reordering, elaborating, or clarifying nodes, emitting up tonRn\_\{R\}variants per prompt each round\. Prompt templates and hyperparameters for SCULPT, OPRO, and EvoPrompt are listed in Appendix[A\.3](https://arxiv.org/html/2606.04661#A1.SS3)\.

### 3\.3Condenser

The condenser lowers prompt\-token cost while preserving task\-relevant instructions\. Our defaultDISTILLreuses SCULPT’s critic\-actor scaffold for its precision and stability, making it structure\-aware by design\. Token\-level compressors such as LLMLingua\-2 drop low\-information surface tokens and can discard task\-critical instructions; DISTILL instead edits the parsed prompt tree: the critic flags redundant or verbose substructures, and the actor applies the tree\-level edits listed in Table[6](https://arxiv.org/html/2606.04661#A1.T6), which update, delete, or merge nodes\. Each round, every prompt is condensed atnCn\_\{C\}compression ratios sampled from a fixed interval \(Appendix[A\.3](https://arxiv.org/html/2606.04661#A1.SS3)\)\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x3.png)Figure 3:Pareto\-gap acquisition geometry\. Dots mark candidate means at normalized costc~i\\tilde\{c\}\_\{i\}; grey arrows extend means byβt​σi,t\\beta\_\{t\}\\sigma\_\{i,t\}to UCB tips at optimistic scorep~i,t\\tilde\{p\}\_\{i,t\}\. Orange tips form the optimistic candidate frontℱt\+\\mathcal\{F\}^\{\+\}\_\{t\}; pink tips lie below it\. For candidatePiP\_\{i\}, the dashed L\-shape to nearest front tipPyP\_\{y\}has lengthgi=Δ​c~\+Δ​p~g\_\{i\}=\\Delta\\tilde\{c\}\+\\Delta\\tilde\{p\}\.
### 3\.4Pareto\-Gap Acquisition Function

Candidate generation by the refiner and condenser uses optimizer\-LLM calls, but it is cheaper than scoring many candidates with target\-LLM calls over validation examples\. Scoring every prompt in𝒬t\\mathcal\{Q\}\_\{t\}on all of𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}would consume the per\-round validation budget many times over\. CRAFT therefore validates a budgeted subset each round and scores each selected candidate on the current validation subset\. We partition𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}once intoTTsubsets\{𝒱j\}j=1T\\\{\\mathcal\{V\}\_\{j\}\\\}\_\{j=1\}^\{T\}bykk\-means clustering; roundttuses subset𝒱π​\(t\)\\mathcal\{V\}\_\{\\pi\(t\)\}, cycling through them withπ​\(t\)=\(\(t−1\)modT\)\+1\\pi\(t\)=\(\(t\-1\)\\bmod T\)\+1\. This shrinks per\-validation cost by a factor ofTT; subset sizes and the rotation schedule are detailed in Appendix[A\.4](https://arxiv.org/html/2606.04661#A1.SS4)\.

Because the true Pareto front is unknown during search, CRAFT spends the per\-round validation budget*optimistically*\. For each candidatePiP\_\{i\}it keeps a running meanμi,t\\mu\_\{i,t\}and standard deviationσi,t\\sigma\_\{i,t\}of the per\-example scores observed so far \(formulas in Appendix[A\.2\.2](https://arxiv.org/html/2606.04661#A1.SS2.SSS2)\), and combines them into an Upper Confidence Bound \(UCB\) scorepi,t\+=μi,t\+βt​σi,tp^\{\+\}\_\{i,t\}=\\mu\_\{i,t\}\+\\beta\_\{t\}\\sigma\_\{i,t\}\. A candidate with few observations has a largeσi,t\\sigma\_\{i,t\}, so it is judged as if its true score sat at the optimistic end of its plausible range\. The weightβt\\beta\_\{t\}falls linearly from near11in the first round to0\.50\.5in the last, tilting the search from exploration toward exploitation\. A brand\-new candidate has no observations at all \(we initializeμi,t=0\\mu\_\{i,t\}\{=\}0,σi,t=1\\sigma\_\{i,t\}\{=\}1\), so it receives the default exploratory scoreβt\\beta\_\{t\}\. We denote by𝒮i,t\\mathcal\{S\}\_\{i,t\}the observation set ofPiP\_\{i\}, i\.e\., the validation examples on which it has been scored through roundtt\.

Algorithm 1Pareto\-Gap UCB Acquisition1:Current candidates

𝒬t\\mathcal\{Q\}\_\{t\}, means

\{μi,t\}\\\{\\mu\_\{i,t\}\\\}, empirical stds

\{σi,t\}\\\{\\sigma\_\{i,t\}\\\}, costs

\{ci\}\\\{c\_\{i\}\\\}, observation sets

\{𝒮i,t\}\\\{\\mathcal\{S\}\_\{i,t\}\\\}, validation batch size

BB, round

tt, subset count

TT
2:Evaluation batch

ℰt\\mathcal\{E\}\_\{t\}with

\|ℰt\|≤B\|\\mathcal\{E\}\_\{t\}\|\\leq B
3:Compute

βt\\beta\_\{t\}and

pi,t\+=μi,t\+βt​σi,tp^\{\+\}\_\{i,t\}=\\mu\_\{i,t\}\+\\beta\_\{t\}\\sigma\_\{i,t\}for all

Pi∈𝒬tP\_\{i\}\\in\\mathcal\{Q\}\_\{t\}
4:Min\-max normalize

\{pi,t\+\}\\\{p^\{\+\}\_\{i,t\}\\\}and

\{ci\}\\\{c\_\{i\}\\\}over

𝒬t\\mathcal\{Q\}\_\{t\}to obtain

\(p~i,t,c~i\)\(\\tilde\{p\}\_\{i,t\},\\tilde\{c\}\_\{i\}\)
5:

ℱt\+←ParetoFront​\(\{\(p~i,t,c~i\):Pi∈𝒬t\}\)\\mathcal\{F\}^\{\+\}\_\{t\}\\leftarrow\\textsc\{ParetoFront\}\\big\(\\\{\(\\tilde\{p\}\_\{i,t\},\\tilde\{c\}\_\{i\}\):P\_\{i\}\\in\\mathcal\{Q\}\_\{t\}\\\}\\big\)
6:foreach candidate

Pi∈𝒬tP\_\{i\}\\in\\mathcal\{Q\}\_\{t\}do

7:

gi←minPy∈ℱt\+⁡\[max⁡\(0,p~y,t−p~i,t\)\+max⁡\(0,c~i−c~y\)\]g\_\{i\}\\leftarrow\\min\\limits\_\{P\_\{y\}\\in\\mathcal\{F\}^\{\+\}\_\{t\}\}\\big\[\\max\(0,\\tilde\{p\}\_\{y,t\}\-\\tilde\{p\}\_\{i,t\}\)\+\\max\(0,\\tilde\{c\}\_\{i\}\-\\tilde\{c\}\_\{y\}\)\\big\]
8:endfor

9:Sort

𝒬t\\mathcal\{Q\}\_\{t\}by ascending

gig\_\{i\}, then descending

pi,t\+p^\{\+\}\_\{i,t\}, then ascending

cic\_\{i\}, then ascending

\|𝒮i,t\|\|\\mathcal\{S\}\_\{i,t\}\|, then stable prompt ID

10:returnthe first

BBcandidates as

ℰt\\mathcal\{E\}\_\{t\}

The UCB score ranks candidates by their optimistic estimate alone; CRAFT also favors the ones that would extend the*front*\. It pairs each UCB score with the candidate’s cost and min\-max normalizes both over the current candidate set, placingPiP\_\{i\}at\(p~i,t,c~i\)\(\\tilde\{p\}\_\{i,t\},\\tilde\{c\}\_\{i\}\)\. In Figure[3](https://arxiv.org/html/2606.04661#S3.F3), the non\-dominated points, drawn as orange UCB tips, form a temporary, optimistic candidate frontℱt\+\\mathcal\{F\}^\{\+\}\_\{t\}\. The*Pareto gap*gig\_\{i\}then measures how far an off\-front candidate sits fromℱt\+\\mathcal\{F\}^\{\+\}\_\{t\}, as the Manhattan distance to the nearest front point within the dominated quadrant, shown as a dashed L\-shape fromPiP\_\{i\}to its nearest front tipPyP\_\{y\}:

gi=miny∈ℱt\+⁡\[max⁡\(0,p~y,t−p~i,t\)\+max⁡\(0,c~i−c~y\)\]\.g\_\{i\}=\\min\_\{y\\in\\mathcal\{F\}^\{\+\}\_\{t\}\}\\\!\\big\[\\,\\max\(0,\\tilde\{p\}\_\{y,t\}\\\!\-\\\!\\tilde\{p\}\_\{i,t\}\)\+\\max\(0,\\tilde\{c\}\_\{i\}\\\!\-\\\!\\tilde\{c\}\_\{y\}\)\\,\\big\]\.A candidate already on the front hasgi=0g\_\{i\}=0; the smaller its gap, the more likely validating it is to improve the retained front\. Brand\-new candidates all share the UCB scoreβt\\beta\_\{t\}, so among them the gap reduces to a preference for cheaper prompts until observations accrue\. In Algorithm[1](https://arxiv.org/html/2606.04661#alg1), we rank𝒬t\\mathcal\{Q\}\_\{t\}by ascending gap and take theBBsmallest as the round’s validation batchℰt\\mathcal\{E\}\_\{t\}\. We setB=2​kB=2k, twice the retained population, letting the selector pick a non\-dominated, spread\-out subset without inflating validation cost\. After scoring, a batch\-relative step prunes consistently weak candidates, sparing later rounds from re\-exploring them \(Appendix[A\.5](https://arxiv.org/html/2606.04661#A1.SS5)\)\.

### 3\.5Selector

Selection by a fixed scalar reward exhibits*scalarization collapse*\. Instead, the selector retains a population that is non\-dominated and spread out, so thekkprompts carried to the next round span diverse accuracy\-cost trade\-offs\. We use the non\-dominated sorting of NSGA\-II\(Debet al\.,[2002](https://arxiv.org/html/2606.04661#bib.bib240)\), which partitions candidates by their\(μi,ci\)\(\\mu\_\{i\},c\_\{i\}\)pairs into successive Pareto frontsF1,F2,…F\_\{1\},F\_\{2\},\\dots; these fronts are admitted whole, best front first, until the population budget is reached \(Appendix[A\.2\.1](https://arxiv.org/html/2606.04661#A1.SS2.SSS1)\)\. When admitting the next front would overflow the budget, the selector chooses among the candidates on that front \(the*boundary front*FjF\_\{j\}\) by a*maximin spread rule*\(Gonzalez,[1985](https://arxiv.org/html/2606.04661#bib.bib262)\): starting from the two objective extremes ofFjF\_\{j\}\(highestμ~\\tilde\{\\mu\}and lowestc~\\tilde\{c\}\), it iteratively admits the candidate that maximizes the minimum Euclidean distance to the already\-admitted candidates ofFjF\_\{j\}in normalized\(μ~i,c~i\)\(\\tilde\{\\mu\}\_\{i\},\\tilde\{c\}\_\{i\}\)space, untilkkare filled, spreading the boundary\-front picks across the accuracy\-cost plane\. Algorithm[2](https://arxiv.org/html/2606.04661#alg2)and Figure[7](https://arxiv.org/html/2606.04661#A1.F7)illustrate the selection process\.

##### The Full Loop\.

Figure[2](https://arxiv.org/html/2606.04661#S1.F2)shows the round\-by\-round loop\. AfterRRrounds CRAFT returns𝒫R\\mathcal\{P\}\_\{R\}, a finite approximation to the accuracy\-cost Pareto front; Table[4](https://arxiv.org/html/2606.04661#A1.T4)in Appendix[A\.1](https://arxiv.org/html/2606.04661#A1.SS1)collects all symbols\. Two choices set CRAFT apart from prior multi\-objective prompt optimization: candidates come from complementary accuracy\-oriented and cost\-oriented generators rather than from one mutation source, and the front\-relative gap decides*which*candidates receive target\-LLM validation in each round rather than allocating those validations by a scalar score over the candidate pool\.

## 4Experiments and Evaluation

### 4\.1Datasets

We evaluate CRAFT on six English classification and reasoning datasets: BeaverTails\(Jiet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib228)\), GoEmotions\(Demszkyet al\.,[2020](https://arxiv.org/html/2606.04661#bib.bib227)\), and four BIG\-Bench Hard tasks \(DisambiguationQA, Causal Judgement, Formal Fallacies, Salient Translation\)\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)\. We use the dataset abbreviations BT, GoE, DQA, CJ, FF, and ST throughout\. Initial prompts for each dataset follow the public release ofKumaret al\.\([2025](https://arxiv.org/html/2606.04661#bib.bib234)\)so that all methods start from the same point\. Full per\-dataset validation/test sizes, task\-score definitions, and task details are in Appendix[B\.1](https://arxiv.org/html/2606.04661#A2.SS1)\.

### 4\.2Setup

CRAFT uses LLMs in two roles: an*optimizer LLM*powers the critic and actor inside the refiner and condenser \(i\.e\., it proposes prompt edits\), and a*target LLM*executes candidate prompts on validation/test examples to score them\. Main comparisons, ablations, and the population\-size sweep use OpenAI GPT\-5\(Singhet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib215)\)as both optimizer and target; the cross\-LLM study fixes the target to GPT\-5\.4\-mini and varies only the optimizer\. The optimizer LLM uses temperature 0\.7 to diversify generated candidates; the target LLM scores with temperature 0\. The main method comparison averages two seeds; the ablation, population\-size, and cross\-LLM studies report a single seed\.

Algorithm 2CRAFT Selection Procedure1:Candidates

\{\(μi,ci\)\}i=12​k\\\{\(\\mu\_\{i\},c\_\{i\}\)\\\}\_\{i=1\}^\{2k\}, population size

kk
2:Compute

\(μ~i,c~i\)\(\\tilde\{\\mu\}\_\{i\},\\tilde\{c\}\_\{i\}\)by min\-max normalizing

\{μi\},\{ci\}\\\{\\mu\_\{i\}\\\},\\\{c\_\{i\}\\\}
3:

\{F1,F2,…\}←FastNonDominatedSort​\(\{\(μi,ci\)\}\)\\\{F\_\{1\},F\_\{2\},\\dots\\\}\\leftarrow\\textsc\{FastNonDominatedSort\}\(\\\{\(\\mu\_\{i\},c\_\{i\}\)\\\}\)
4:

𝒫t←∅\\mathcal\{P\}\_\{t\}\\leftarrow\\emptyset;

j←1j\\leftarrow 1
5:while

\|𝒫t\|\+\|Fj\|≤k\|\\mathcal\{P\}\_\{t\}\|\+\|F\_\{j\}\|\\leq kdo

6:

𝒫t←𝒫t∪Fj\\mathcal\{P\}\_\{t\}\\leftarrow\\mathcal\{P\}\_\{t\}\\cup F\_\{j\};

j←j\+1j\\leftarrow j\+1
7:endwhile

8:if

\|𝒫t\|<k\|\\mathcal\{P\}\_\{t\}\|<kthen⊳\\trianglerightpartial fill fromFjF\_\{j\}by maximin spread

9:

r←k−\|𝒫t\|r\\leftarrow k\-\|\\mathcal\{P\}\_\{t\}\|⊳\\trianglerightstill to fill

10:

S←S\\leftarrowup to

min⁡\(2,r\)\\min\(2,r\)objective\-extreme candidates of

FjF\_\{j\}
11:while

\|S\|<r\|S\|<rand

Fj∖S≠∅F\_\{j\}\\setminus S\\neq\\emptysetdo

12:

i∗←arg​maxi∈Fj∖S⁡mins∈S⁡‖\(μ~i,c~i\)−\(μ~s,c~s\)‖2i^\{\*\}\\leftarrow\\operatorname\*\{arg\\,max\}\\limits\_\{i\\in F\_\{j\}\\setminus S\}\\ \\min\\limits\_\{s\\in S\}\\ \\\|\(\\tilde\{\\mu\}\_\{i\},\\tilde\{c\}\_\{i\}\)\-\(\\tilde\{\\mu\}\_\{s\},\\tilde\{c\}\_\{s\}\)\\\|\_\{2\}
13:

S←S∪\{i∗\}S\\leftarrow S\\cup\\\{i^\{\*\}\\\}
14:endwhile

15:

𝒫t←𝒫t∪S\\mathcal\{P\}\_\{t\}\\leftarrow\\mathcal\{P\}\_\{t\}\\cup S
16:endif

17:return

𝒫t\\mathcal\{P\}\_\{t\}

We setR=8R=8for all method comparisons; diagnostic figures use extended runs where noted, and §[5](https://arxiv.org/html/2606.04661#S5.SS0.SSS0.Px6)shows best score and hypervolume flatten nearR=8R=8\. Per prompt in the current population, CRAFT’s refiner produces up tonR=8n\_\{R\}=8refined variants and its condensernC=4n\_\{C\}=4condensed variants; with population sizek=4k=4, full CRAFT generates up tok​\(nR\+nC\)k\(n\_\{R\}\{\+\}n\_\{C\}\)new candidates per round and retainskkprompts\.B=2​kB=2kcandidates are validated per round on the round’s subset𝒱π​\(t\)\\mathcal\{V\}\_\{\\pi\(t\)\}, costingB⋅\|𝒱π​\(t\)\|B\\cdot\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|LLM calls\. Across comparison groups we keepRR,kk, the validation\-subset schedule, andBBfixed; generation modules and score objectives vary by method as defined below\. Target\-validation compute is thus comparable; CRAFT’s advantage shows up as wider front coverage and lower deployment\-time prompt\-token cost\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x4.png)Figure 4:Mean rank across the six benchmarks atR=8R\{=\}8\(lower is better\)\. Columns report ranks rather than raw metric values; the left columns group per\-metric ranks into front, score, and cost aspects, and the rightmostOverallcolumn is the composite rank with the three aspects weighted equally, lowest for CRAFT\.
### 4\.3Variants and Baselines

We compare CRAFT with two baseline families and two component ablations\.

##### Weighted\-Sum Scalarization \(WPRO\)\.

CAPO scalarizes accuracy against a length\-penalty term using a hyperparameterγ\\gammafixed before search\. Because accuracy and token\-length ranges differ across datasets, one fixedγ\\gammadoes not transfer; we address this by min\-max\-normalizing both axes over the current candidate set and taking a weighted sum, which we call WPRO\. It scores each candidatePiP\_\{i\}byScore​\(Pi\)=wp​p^i\+wc​c^i\\mathrm\{Score\}\(P\_\{i\}\)=w\_\{p\}\\hat\{p\}\_\{i\}\+w\_\{c\}\\hat\{c\}\_\{i\}, wherep^i\\hat\{p\}\_\{i\}andc^i\\hat\{c\}\_\{i\}are normalized accuracy and token reduction \(both larger\-is\-better; formulas in Appendix[A\.3](https://arxiv.org/html/2606.04661#A1.SS3)\)\. In WPRO, scalarization is used both when allocating validation and when retaining the population\. For acquisition, we replace Pareto\-gap UCB with a weighted\-sum UCB score over normalized optimistic accuracy and token reduction; for retention, we sort validated candidates by the corresponding weighted score over empirical mean accuracy and token reduction and keep the topkk\. The refiner, condenser, validation subsets, and per\-round validation batch size match CRAFT\. Because the weight is still fixed before search, WPRO often recovers only a narrow region of the front \(Figure[1](https://arxiv.org/html/2606.04661#S1.F1)\), our empirical instance of*scalarization collapse*\. We sweepwp∈\{0\.3,0\.5,0\.7\}w\_\{p\}\\in\\\{0\.3,0\.5,0\.7\\\}withwc=1−wpw\_\{c\}=1\-w\_\{p\}to probe cost\-leaning, balanced, and score\-leaning regimes of the trade\-off\.

##### Single\-Axis Baselines\.

Single\-axis baselines run inside CRAFT’s loop \(same validation subsets and per\-round budget\) but use one generator family at a time and score\-only acquisition/retention\(Pryzantet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib15); Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\), with no cost objective\. Validation is allocated by score\-only UCB, and the topkkcandidates by empirical mean task score are retained\. SCULPT uses the accuracy\-oriented refiner alone; DISTILL and LLMLingua use cost\-oriented compression generators alone\. Full setup details are in Appendix[A\.3](https://arxiv.org/html/2606.04661#A1.SS3)\.

##### Component Ablations of CRAFT\.

We isolate each generation module with two ablations: CRAFT\-R keeps only the refiner \(SCULPT, no condenser\), and CRAFT\-C keeps only the condenser \(DISTILL, no refiner\)\. To probe how much the refiner matters, we also run two alternate\-refiner variants, CRAFTOPRO\{\}\_\{\\text\{OPRO\}\}and CRAFTEvo\{\}\_\{\\text\{Evo\}\}, which replace the default SCULPT refiner with OPRO and EvoPrompt respectively while keeping the condenser, acquisition, and selector unchanged\. Unlike the single\-axis baselines, these ablations keep CRAFT’s Pareto\-gap acquisition and NSGA\-II selector\.

### 4\.4Evaluation Metrics

At the defaultR=8R=8snapshot, we report seven metrics covering score, cost, and front coverage\. A prompt is*feasible*if its test score is at least0\.95×0\.95\\timesthe initial\-prompt test score; cost\-leaning metrics use this filter to enforce the deployment floor below which cost savings are rarely worth the accuracy drop\. This feasibility check is a reporting filter applied when computing metrics; it is not the in\-loop pruning rule used during optimization \(Appendix[A\.5](https://arxiv.org/html/2606.04661#A1.SS5)\)\. The seven metrics are:Best score\(max task score in the retained population\),Mean retained\-population score\(Meanin tables and figures\),Min feasible tokens\(Tok\),Peak efficiency\(Eff =EmaxE\_\{\\max\}; the score\-per\-token ratio reported in percent\-score\-points per 100 tokens, i\.e\.,Emax=100⋅pi∗/ci∗E\_\{\\max\}=100\\cdot p\_\{i^\{\*\}\}/c\_\{i^\{\*\}\}wherei∗=arg⁡maxi⁡pi/cii^\{\*\}=\\arg\\max\_\{i\}p\_\{i\}/c\_\{i\}\),HypervolumeHV\(Zitzler and Thiele,[1999](https://arxiv.org/html/2606.04661#bib.bib250)\)relative to the initial prompt,Inverted Generational DistanceIGD\(Bosman and Thierens,[2003](https://arxiv.org/html/2606.04661#bib.bib255)\)against the method\-union front, andFront size\|ℱ\|\|\\mathcal\{F\}\|\. Full per\-metric definitions, the HV reference choice, and the method\-union IGD justification are in Appendix[B\.2](https://arxiv.org/html/2606.04661#A2.SS2)\. The*composite rank*aggregates per\-metric ranks across three aspects of equal weight: front quality𝒜q=\{HV,\|ℱ\|,IGD\}\\mathcal\{A\}\_\{\\mathrm\{q\}\}=\\\{\\text\{HV\},\|\\mathcal\{F\}\|,\\text\{IGD\}\\\}, score𝒜s=\{best,mean\}\\mathcal\{A\}\_\{\\mathrm\{s\}\}=\\\{\\text\{best\},\\text\{mean\}\\\}, and cost𝒜c=\{Emax,tokens\}\\mathcal\{A\}\_\{\\mathrm\{c\}\}=\\\{E\_\{\\max\},\\text\{tokens\}\\\}\.

Composite​\(m\)=13​\|D\|​∑d∈D∑𝒜r𝒜​\(m,d\),\\mathrm\{Composite\}\(m\)=\\frac\{1\}\{3\|D\|\}\\sum\_\{d\\in D\}\\sum\_\{\\mathcal\{A\}\}r\_\{\\mathcal\{A\}\}\(m,d\),\(1\)
wherer𝒜​\(m,d\)r\_\{\\mathcal\{A\}\}\(m,d\)is the mean per\-metric rank of methodmmon datasetddwithin aspect𝒜\\mathcal\{A\}\.

## 5Results

##### Method Comparison\.

Figure[4](https://arxiv.org/html/2606.04661#S4.F4)reports each method’s mean rank on every metric across the six datasets and aggregates them into the composite rank \(rightmost column\)\. Figure[9](https://arxiv.org/html/2606.04661#A3.F9)gives per\-dataset composite ranks; Table[8](https://arxiv.org/html/2606.04661#A3.T8)reports the absolute per\-dataset values \(Appendix[C\.1](https://arxiv.org/html/2606.04661#A3.SS1)\)\. The baselines exhibit*scalarization collapse*\. Single\-axis baselines rank near the top of the axis they emphasize \(SCULPT 2nd on score, DISTILL 2nd on cost\) but trail on the others, and LLMLingua fares worst because many of its compressed prompts fall below the feasibility threshold and lose even on cost\. Weighted\-sum baselines collapse along the trade\-off weight: each WPRO variant leads the axis its weight favors but trails the other, and even the balanced WPRO0\.5only reaches 3rd on the composite rank\.CRAFT ranks 1st on the overall composite rank\.It does not win every metric, placing 3rd on cost behind baselines with cost\-oriented generators, but maintains coverage of both high\-accuracy and low\-token regions: Figure[1](https://arxiv.org/html/2606.04661#S1.F1)shows on BT that each baseline confines its retained set to one region while CRAFT’s retained set covers both ends\. Per\-dataset rankings \(Figure[9](https://arxiv.org/html/2606.04661#A3.F9)\) further show this lead reflects robustness across the three aspects rather than dominance on any individual dataset\.

##### Front Evolution\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x5.png)Figure 5:CRAFT’s retained set on DQA across rounds\. Non\-dominated points have darker outlines; dominated ones are smaller; the gold star marks the initial prompt\.Figure[5](https://arxiv.org/html/2606.04661#S5.F5)visualizes the prompts CRAFT selects across an extended 12\-round DQA run, colored by round\. The selected prompts move toward the upper\-left region of high accuracy and low cost: later rounds \(lighter\) reach both higher accuracy and lower cost than the initial prompt \(gold star\), and each round’s non\-dominated candidates spread along the trade\-off rather than piling at a single corner\. Per\-metric trajectories across all six benchmarks \(Appendix[C\.2](https://arxiv.org/html/2606.04661#A3.SS2)\) improve overall but non\-monotonically, as refinement and condensation alternately add and remove structure\.

DataSettingBest↑\\uparrowMean↑\\uparrowTok↓\\downarrowEff↑\\uparrowHV↑\\uparrow\|ℱ\|\|\\mathcal\{F\}\|↑\\uparrowBTCRAFT\-R63\.061\.51,0136\.262k3CRAFT\-C53\.052\.227919\.052k1CRAFT63\.061\.751212\.363k3CRAFTOPRO\{\}\_\{\\text\{OPRO\}\}59\.057\.35909\.557k2CRAFTEvo\{\}\_\{\\text\{Evo\}\}54\.053\.532616\.353k1GoECRAFT\-R41\.040\.52,1301\.939k2CRAFT\-C32\.031\.04008\.031k2CRAFT37\.035\.05636\.636k2CRAFTOPRO\{\}\_\{\\text\{OPRO\}\}38\.036\.831811\.338k3CRAFTEvo\{\}\_\{\\text\{Evo\}\}36\.034\.84557\.335k2

Table 1:Ablation of CRAFT on BT and GoE\. CRAFT\-R retains the refiner only; CRAFT\-C retains the condenser only\. CRAFTOPRO\{\}\_\{\\text\{OPRO\}\}and CRAFTEvo\{\}\_\{\\text\{Evo\}\}replace the default SCULPT refiner with OPRO and EvoPrompt\. Front size counts feasible prompts only\.
##### Ablation Study\.

To isolate the contribution of each generation module, we run two CRAFT variants: CRAFT\-R retains only the refiner; CRAFT\-C retains only the condenser\. CRAFT\-R matches the full CRAFT on accuracy and front size, but its prompts grow to1,0131\{,\}013tokens on BT and2,1302\{,\}130on GoE, far longer than the full CRAFT \(512512and563563\), because the refiner has no cost counterweight\. CRAFT\-C produces the shortest prompts but reduces the best score by1010points on BT and55on GoE, and on BT its front collapses to a single feasible prompt as aggressive compression pushes most variants below the feasibility threshold\. Neither module suffices alone, since the refiner recovers accuracy but inflates length while the condenser shortens prompts but cannot recover score; only the full CRAFT balances both axes\.

##### Impact of Refiner\.

Table[1](https://arxiv.org/html/2606.04661#S5.T1)also reports two CRAFT variants that change only the refiner, replacing SCULPT with OPRO or EvoPrompt while keeping the condenser, acquisition, and selector fixed\. CRAFTOPRO\{\}\_\{\\text\{OPRO\}\}matches or surpasses CRAFT on GoE while trailing on BT, plausibly because OPRO uses prior prompts and their validation scores to guide refinement\. CRAFTEvo\{\}\_\{\\text\{Evo\}\}improves over the initial prompt on GoE but lags on BT\. Together they show that CRAFT accommodates alternative refiners without retuning the loop, although the choice of refiner affects which dataset gains most\.

OptimizerBest↑\\uparrowMean↑\\uparrowTok↓\\downarrowEff↑\\uparrowHV↑\\uparrow\|ℱ\|\|\\mathcal\{F\}\|↑\\uparrowInitial36\.536\.57944\.6n/a1CRAFT5\.553\.038\.85469\.752k4CRAFT5\.451\.035\.55629\.150k3CRAFTmini\{\}\_\{\\text\{mini\}\}48\.034\.85738\.446k3CRAFTDS\{\}\_\{\\text\{DS\}\}51\.036\.050210\.251k4CRAFTKimi\{\}\_\{\\text\{Kimi\}\}52\.044\.86907\.550k3Table 2:Cross\-LLM transfer on GoE with GPT\-5\.4\-mini as the fixed target\. Optimizer subscripts:5\.55\.5= GPT\-5\.5,5\.45\.4= GPT\-5\.4, mini = GPT\-5\.4\-mini, DS = DeepSeek\-V4 Flash, Kimi = Kimi\-K2\.5\.
##### Cross\-LLM Transfer\.

CRAFT’s search operators depend on the optimizer LLM; the target LLM is held fixed while prompts are optimized\. The main results use GPT\-5 as both optimizer and target\. To study the impact of the optimizer LLM, we fix the target at GPT\-5\.4\-mini and run CRAFT with five optimizers: GPT\-5\.5, GPT\-5\.4, GPT\-5\.4\-mini, DeepSeek\-V4 Flash\(DeepSeek\-AI,[2026](https://arxiv.org/html/2606.04661#bib.bib217)\), and Kimi\-K2\.5\(Teamet al\.,[2026](https://arxiv.org/html/2606.04661#bib.bib216)\)\. On GoE \(Table[2](https://arxiv.org/html/2606.04661#S5.T2)\), every tested optimizer expands the front from the initial prompt, improving best score, peak efficiency, and hypervolume while reducing prompt\-token cost, so CRAFT’s gain is not tied to matching optimizer and target, and works across optimizer LLM families\. Optimizer choice shifts which metric leads: GPT\-5\.5 leads on best score and hypervolume, DeepSeek\-V4 Flash on prompt\-token cost and peak efficiency, and Kimi\-K2\.5 on mean retained\-population score, so CRAFT’s front gains carry across optimizer families even when no one optimizer dominates every axis\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x6.png)Figure 6:CRAFT hypervolume \(↑\\uparrow\) and best score \(↑\\uparrow\) over rounds0to1212on BT and GoE\.
##### Impact of Round Budget\.

To justify theR=8R=8default, we extend CRAFT toR=12R\{=\}12on BT and GoE and track hypervolume and best score round by round\. In Figure[6](https://arxiv.org/html/2606.04661#S5.F6), both metrics rise sharply early and flatten nearR=8R=8; the four extra rounds bring oscillation rather than steady gains\. Reporting atR=8R=8captures most progress while keeping cost comparable across baselines\.

SettingBest↑\\uparrowMean↑\\uparrowTok↓\\downarrowEff↑\\uparrowHV↑\\uparrow\|ℱ\|\|\\mathcal\{F\}\|↑\\uparrowBT,k=2k\{=\}258\.057\.038814\.958k2BT,k=4k\{=\}463\.061\.751212\.363k3BT,k=6k\{=\}661\.058\.334917\.561k4BT,k=8k\{=\}854\.052\.124422\.152k2GoE,k=2k\{=\}237\.034\.56026\.137k2GoE,k=4k\{=\}437\.035\.05636\.636k2GoE,k=6k\{=\}640\.035\.38604\.740k3GoE,k=8k\{=\}842\.036\.34357\.437k4Table 3:Population\-size \(kk\) sweep for CRAFT\.
##### Impact of Population Size\.

The retained\-population sizekksets how many prompts the optimizer keeps each round\. We usek=4k=4as the default to leave room for high\-accuracy, short, balanced, and intermediate prompts in the retained population\. Table[3](https://arxiv.org/html/2606.04661#S5.T3)sweepsk∈\{2,4,6,8\}k\\in\\\{2,4,6,8\\\}:k=2k=2is too small to cover both axes, while largerkktrades peak accuracy for broader or cheaper fronts\. The two datasets respond differently: BT peaks atk=4k=4on best score and hypervolume but reaches its lowest token count and highest efficiency atk=8k=8, while GoE improves nearly monotonically, winning best score, efficiency, and front size atk=8k=8\. The bestkktherefore depends on whether score, cost, or front coverage matters most;k=4k=4is a balanced default across all six benchmarks\.

## 6Conclusion

In summary, CRAFT demonstrates that cost\-aware prompt optimization is more reliably addressed as Pareto\-front search than as scalarized optimization\. In our experiments, accuracy\-only, cost\-only, and weighted\-sum baselines tend to concentrate in one region of the accuracy\-cost front\. CRAFT does not win every metric, yet it remains competitive on each of front quality, task score, and cost and produces the strongest overall trade\-offs, a balance that is preserved when the optimizer LLM is varied\. The ablations show that the refiner and the condenser play complementary roles, since removing either restricts the candidate set available to the acquisition function, and only their combination provides the diversity needed to extend the front\. The loop itself is not tied to SCULPT or to any fixed implementation of its components, so alternative refiners or condensers can be plugged into the same front\-aware procedure\. CRAFT is therefore most useful when the accuracy\-cost trade\-off is unknown a priori or varies across deployments\.

## 7Limitations

CRAFT has several limitations\. First, our evaluation is restricted to English classification and short\-answer reasoning benchmarks\. As a result, we cannot yet determine whether CRAFT generalizes to more open\-ended generation settings, such as summarization, code generation, dialogue, or multilingual prompting\. Second, several aspects of our experimental setup remain fixed\. While we vary the optimizer LLM \(§[5](https://arxiv.org/html/2606.04661#S5.SS0.SSS0.Px5)\), the target model is kept within the OpenAI family\. Evaluating CRAFT on non\-OpenAI targets, such as Claude or Gemini, as well as open\-source model families including Llama, Qwen, and Mistral, remains an important direction for future work\. Similarly, we do not study smaller target models in the 1B–7B parameter range\.

Third, our main experiments use one default refiner and one default condenser, both powered by the same optimizer LLM\. We partially examine the role of the refiner by replacing SCULPT with OPRO and EvoPrompt \(§[5](https://arxiv.org/html/2606.04661#S5.SS0.SSS0.Px3)\)\. On the compression side, LLMLingua\-2 serves as a token\-level alternative to DISTILL; however, its relatively weak performance led us not to explore additional compressors within CRAFT\. Future work could investigate history\-aware compressors inspired by OPRO, evolutionary compressors based on EvoPrompt, or alternative generator LLMs for both modules\. Finally, CRAFT assumes a minimally task\-relevant initial prompt\. Its behavior under very weak, underspecified, or adversarial initial prompts remains unexplored\.

## References

- L\. A\. Agrawal, S\. Tan, D\. Soylu, N\. Ziems, R\. Khare, K\. Opsahl\-Ong, A\. Singhvi, H\. Shandilya, M\. J\. Ryan, M\. Jiang, C\. Potts, K\. Sen, A\. Dimakis, I\. Stoica, D\. Klein, M\. Zaharia, and O\. Khattab \(2026\)GEPA: reflective prompt evolution can outperform reinforcement learning\.InThe Fourteenth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=RQm2KQTM5r)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- Finite\-time analysis of the multiarmed bandit problem\.Machine learning47\(2\),pp\. 235–256\.Cited by:[§A\.2\.2](https://arxiv.org/html/2606.04661#A1.SS2.SSS2.p1.6)\.
- P\. A\. N\. Bosman and D\. Thierens \(2003\)The balance between proximity and diversity in multiobjective evolutionary algorithms\.IEEE Transactions on Evolutionary Computation7\(2\),pp\. 174–188\.Cited by:[6th item](https://arxiv.org/html/2606.04661#A2.I1.i6.p1.5),[§4\.4](https://arxiv.org/html/2606.04661#S4.SS4.p1.9)\.
- L\. Chen, M\. Zaharia, and J\. Zou \(2024\)FrugalGPT: how to use large language models while reducing cost and improving performance\.Transactions on Machine Learning Research\.Note:Featured CertificationExternal Links:ISSN 2835\-8856,[Link](https://openreview.net/forum?id=cSimKw5p6R)Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px4.p1.1)\.
- I\. Das and J\. E\. Dennis \(1997\)A closer look at drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems\.Structural optimization14\(1\),pp\. 63–69\.Cited by:[§A\.2](https://arxiv.org/html/2606.04661#A1.SS2.SSS0.Px1.p1.3),[§1](https://arxiv.org/html/2606.04661#S1.p3.1)\.
- S\. Daulton, M\. Balandat, and E\. Bakshy \(2021\)Parallel bayesian optimization of multiple noisy objectives with expected hypervolume improvement\.InAdvances in Neural Information Processing Systems,M\. Ranzato, A\. Beygelzimer, Y\. Dauphin, P\.S\. Liang, and J\. W\. Vaughan \(Eds\.\),Vol\.34,pp\. 2187–2200\.External Links:[Link](https://proceedings.neurips.cc/paper_files/paper/2021/file/11704817e347269b7254e744b5e22dac-Paper.pdf)Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p4.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px4.p1.1)\.
- K\. Deb, A\. Pratap, S\. Agarwal, and T\. Meyarivan \(2002\)A fast and elitist multiobjective genetic algorithm: nsga\-ii\.IEEE transactions on evolutionary computation6\(2\),pp\. 182–197\.Cited by:[§A\.2\.1](https://arxiv.org/html/2606.04661#A1.SS2.SSS1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p4.1),[§3\.5](https://arxiv.org/html/2606.04661#S3.SS5.p1.10)\.
- DeepSeek\-AI \(2026\)DeepSeek\-v4: towards highly efficient million\-token context intelligence\.Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2606.04661#S5.SS0.SSS0.Px5.p1.1)\.
- D\. Demszky, D\. Movshovitz\-Attias, J\. Ko, A\. Cowen, G\. Nemade, and S\. Ravi \(2020\)GoEmotions: a dataset of fine\-grained emotions\.InProceedings of the 58th Annual Meeting of the Association for Computational Linguistics,D\. Jurafsky, J\. Chai, N\. Schluter, and J\. Tetreault \(Eds\.\),Online,pp\. 4040–4054\.External Links:[Link](https://aclanthology.org/2020.acl-main.372/),[Document](https://dx.doi.org/10.18653/v1/2020.acl-main.372)Cited by:[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px2.p1.1),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2606.04661#S4.SS1.p1.1)\.
- M\. Deng, J\. Wang, C\. Hsieh, Y\. Wang, H\. Guo, T\. Shu, M\. Song, E\. Xing, and Z\. Hu \(2022\)RLPrompt: optimizing discrete text prompts with reinforcement learning\.InProceedings of the 2022 Conference on Empirical Methods in Natural Language Processing,Y\. Goldberg, Z\. Kozareva, and Y\. Zhang \(Eds\.\),Abu Dhabi, United Arab Emirates,pp\. 3369–3391\.External Links:[Link](https://aclanthology.org/2022.emnlp-main.222/),[Document](https://dx.doi.org/10.18653/v1/2022.emnlp-main.222)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- C\. Fernando, D\. S\. Banarse, H\. Michalewski, S\. Osindero, and T\. Rocktäschel \(2024\)Promptbreeder: self\-referential self\-improvement via prompt evolution\.InProceedings of the 41st International Conference on Machine Learning,R\. Salakhutdinov, Z\. Kolter, K\. Heller, A\. Weller, N\. Oliver, J\. Scarlett, and F\. Berkenkamp \(Eds\.\),Proceedings of Machine Learning Research, Vol\.235,pp\. 13481–13544\.External Links:[Link](https://proceedings.mlr.press/v235/fernando24a.html)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- T\. F\. Gonzalez \(1985\)Clustering to minimize the maximum intercluster distance\.Theoretical computer science38,pp\. 293–306\.Cited by:[§A\.2\.1](https://arxiv.org/html/2606.04661#A1.SS2.SSS1.Px2.p1.16),[§A\.2\.1](https://arxiv.org/html/2606.04661#A1.SS2.SSS1.p1.1),[§3\.5](https://arxiv.org/html/2606.04661#S3.SS5.p1.10)\.
- Q\. Guo, R\. Wang, J\. Guo, B\. Li, K\. Song, X\. Tan, G\. Liu, J\. Bian, and Y\. Yang \(2024\)Connecting large language models with evolutionary algorithms yields powerful prompt optimizers\.InThe Twelfth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=ZG3RaNIsO8)Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- Y\. Jafari, D\. Mekala, R\. Yu, and T\. Berg\-Kirkpatrick \(2024\)MORL\-prompt: an empirical analysis of multi\-objective reinforcement learning for discrete prompt optimization\.InFindings of the Association for Computational Linguistics: EMNLP 2024,Y\. Al\-Onaizan, M\. Bansal, and Y\. Chen \(Eds\.\),Miami, Florida, USA,pp\. 9878–9889\.External Links:[Link](https://aclanthology.org/2024.findings-emnlp.577/),[Document](https://dx.doi.org/10.18653/v1/2024.findings-emnlp.577)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- J\. Ji, M\. Liu, J\. Dai, X\. Pan, C\. Zhang, C\. Bian, B\. Chen, R\. Sun, Y\. Wang, and Y\. Yang \(2023\)Beavertails: towards improved safety alignment of llm via a human\-preference dataset\.Advances in Neural Information Processing Systems36,pp\. 24678–24704\.Cited by:[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px1.p1.1),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2606.04661#S4.SS1.p1.1)\.
- H\. Jiang, Q\. Wu, C\. Lin, Y\. Yang, and L\. Qiu \(2023\)LLMLingua: compressing prompts for accelerated inference of large language models\.InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing,H\. Bouamor, J\. Pino, and K\. Bali \(Eds\.\),Singapore,pp\. 13358–13376\.External Links:[Link](https://aclanthology.org/2023.emnlp-main.825/),[Document](https://dx.doi.org/10.18653/v1/2023.emnlp-main.825)Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px2.p1.1)\.
- Z\. Jiang, F\. F\. Xu, J\. Araki, and G\. Neubig \(2020\)How can we know what language models know?\.Transactions of the Association for Computational Linguistics8,pp\. 423–438\.External Links:ISSN 2307\-387X,[Document](https://dx.doi.org/10.1162/tacl%5Fa%5F00324),[Link](https://doi.org/10.1162/tacl_a_00324)Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p3.1)\.
- O\. Khattab, A\. Singhvi, P\. Maheshwari, Z\. Zhang, K\. Santhanam, S\. V\. A, S\. Haq, A\. Sharma, T\. T\. Joshi, H\. Moazam, H\. Miller, M\. Zaharia, and C\. Potts \(2024\)DSPy: compiling declarative language model calls into state\-of\-the\-art pipelines\.InThe Twelfth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=sY5N0zY5Od)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- J\. Knowles \(2006\)ParEGO: a hybrid algorithm with on\-line landscape approximation for expensive multiobjective optimization problems\.IEEE Transactions on Evolutionary Computation10\(1\),pp\. 50–66\.Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px4.p1.1)\.
- S\. Kumar, A\. Y\. Venkata, S\. Khandelwal, B\. Santra, P\. Agrawal, and M\. Gupta \(2025\)SCULPT: systematic tuning of long prompts\.InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics \(Volume 1: Long Papers\),W\. Che, J\. Nabende, E\. Shutova, and M\. T\. Pilehvar \(Eds\.\),Vienna, Austria,pp\. 14996–15029\.External Links:[Link](https://aclanthology.org/2025.acl-long.730/),[Document](https://dx.doi.org/10.18653/v1/2025.acl-long.730),ISBN 979\-8\-89176\-251\-0Cited by:[§A\.3](https://arxiv.org/html/2606.04661#A1.SS3.SSS0.Px2.p1.1),[§A\.3](https://arxiv.org/html/2606.04661#A1.SS3.SSS0.Px8.p1.2),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1),[§3\.2](https://arxiv.org/html/2606.04661#S3.SS2.p1.1),[§4\.1](https://arxiv.org/html/2606.04661#S4.SS1.p1.1),[§4\.3](https://arxiv.org/html/2606.04661#S4.SS3.SSS0.Px2.p1.1)\.
- J\. MacQueen \(1967\)Some methods for classification and analysis of multivariate observations\.InProceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability,Vol\.1,pp\. 281–297\.Cited by:[§A\.4](https://arxiv.org/html/2606.04661#A1.SS4.SSS0.Px2.p1.7),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px4.p1.4)\.
- Y\. Menchaca Resendiz and R\. Klinger \(2025\)MOPO: multi\-objective prompt optimization for affective text generation\.InProceedings of the 31st International Conference on Computational Linguistics,O\. Rambow, L\. Wanner, M\. Apidianaki, H\. Al\-Khalifa, B\. D\. Eugenio, and S\. Schockaert \(Eds\.\),Abu Dhabi, UAE,pp\. 5588–5606\.External Links:[Link](https://aclanthology.org/2025.coling-main.375/)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- J\. Mu, X\. L\. Li, and N\. Goodman \(2023\)Learning to compress prompts with gist tokens\.InThirty\-seventh Conference on Neural Information Processing Systems,External Links:[Link](https://openreview.net/forum?id=2DtxPCL3T5)Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px2.p1.1)\.
- Z\. Pan, Q\. Wu, H\. Jiang, M\. Xia, X\. Luo, J\. Zhang, Q\. Lin, V\. Rühle, Y\. Yang, C\. Lin, H\. V\. Zhao, L\. Qiu, and D\. Zhang \(2024\)LLMLingua\-2: data distillation for efficient and faithful task\-agnostic prompt compression\.InFindings of the Association for Computational Linguistics: ACL 2024,L\. Ku, A\. Martins, and V\. Srikumar \(Eds\.\),Bangkok, Thailand,pp\. 963–981\.External Links:[Link](https://aclanthology.org/2024.findings-acl.57/),[Document](https://dx.doi.org/10.18653/v1/2024.findings-acl.57)Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px4.p1.4),[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px2.p1.1)\.
- R\. Pryzant, D\. Iter, J\. Li, Y\. Lee, C\. Zhu, and M\. Zeng \(2023\)Automatic prompt optimization with “gradient descent” and beam search\.InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing,H\. Bouamor, J\. Pino, and K\. Bali \(Eds\.\),Singapore,pp\. 7957–7968\.External Links:[Link](https://aclanthology.org/2023.emnlp-main.494/),[Document](https://dx.doi.org/10.18653/v1/2023.emnlp-main.494)Cited by:[§A\.3](https://arxiv.org/html/2606.04661#A1.SS3.SSS0.Px8.p1.2),[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1),[§4\.3](https://arxiv.org/html/2606.04661#S4.SS3.SSS0.Px2.p1.1)\.
- K\. Ramnath, K\. Zhou, S\. Guan, S\. S\. Mishra, X\. Qi, Z\. Shen, S\. Wang, S\. Woo, S\. Jeoung, Y\. Wang,et al\.\(2025\)A systematic survey of automatic prompt optimization techniques\.InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing,pp\. 33066–33098\.Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p1.1)\.
- N\. Reimers and I\. Gurevych \(2019\)Sentence\-BERT: sentence embeddings using Siamese BERT\-networks\.InProceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing \(EMNLP\-IJCNLP\),K\. Inui, J\. Jiang, V\. Ng, and X\. Wan \(Eds\.\),Hong Kong, China,pp\. 3982–3992\.External Links:[Link](https://aclanthology.org/D19-1410/),[Document](https://dx.doi.org/10.18653/v1/D19-1410)Cited by:[§A\.4](https://arxiv.org/html/2606.04661#A1.SS4.SSS0.Px2.p1.7),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px4.p1.4)\.
- T\. Schnabel and J\. Neville \(2024\)Symbolic prompt program search: a structure\-aware approach to efficient compile\-time prompt optimization\.InFindings of the Association for Computational Linguistics: EMNLP 2024,Y\. Al\-Onaizan, M\. Bansal, and Y\. Chen \(Eds\.\),Miami, Florida, USA,pp\. 670–686\.External Links:[Link](https://aclanthology.org/2024.findings-emnlp.37/),[Document](https://dx.doi.org/10.18653/v1/2024.findings-emnlp.37)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- A\. Singh, A\. Fry, A\. Perelman, A\. Tart, A\. Ganesh, A\. El\-Kishky, A\. McLaughlin, A\. Low, A\. Ostrow, A\. Ananthram,et al\.\(2025\)Openai gpt\-5 system card\.arXiv preprint arXiv:2601\.03267\.Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§4\.2](https://arxiv.org/html/2606.04661#S4.SS2.p1.1)\.
- N\. Srinivas, A\. Krause, S\. M\. Kakade, and M\. Seeger \(2009\)Gaussian process optimization in the bandit setting: no regret and experimental design\.arXiv preprint arXiv:0912\.3995\.Cited by:[§A\.2\.2](https://arxiv.org/html/2606.04661#A1.SS2.SSS2.p1.6),[§A\.2\.2](https://arxiv.org/html/2606.04661#A1.SS2.SSS2.p2.9),[§1](https://arxiv.org/html/2606.04661#S1.p4.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px4.p1.1)\.
- M\. Suzgun, N\. Scales, N\. Schärli, S\. Gehrmann, Y\. Tay, H\. W\. Chung, A\. Chowdhery, Q\. Le, E\. Chi, D\. Zhou, and J\. Wei \(2023\)Challenging BIG\-bench tasks and whether chain\-of\-thought can solve them\.InFindings of the Association for Computational Linguistics: ACL 2023,A\. Rogers, J\. Boyd\-Graber, and N\. Okazaki \(Eds\.\),Toronto, Canada,pp\. 13003–13051\.External Links:[Link](https://aclanthology.org/2023.findings-acl.824/),[Document](https://dx.doi.org/10.18653/v1/2023.findings-acl.824)Cited by:[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px3.p1.1),[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px4.p1.1),[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px5.p1.1),[§B\.1](https://arxiv.org/html/2606.04661#A2.SS1.SSS0.Px6.p1.1),[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2606.04661#S4.SS1.p1.1)\.
- K\. Team, T\. Bai, Y\. Bai, Y\. Bao, S\. Cai, Y\. Cao, Y\. Charles, H\. Che, C\. Chen, G\. Chen,et al\.\(2026\)Kimi k2\.5: visual agentic intelligence\.arXiv preprint arXiv:2602\.02276\.Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2606.04661#S5.SS0.SSS0.Px5.p1.1)\.
- Y\. Wen, N\. Jain, J\. Kirchenbauer, M\. Goldblum, J\. Geiping, and T\. Goldstein \(2024\)Hard prompts made easy: gradient\-based discrete optimization for prompt tuning and discovery\.Advances in Neural Information Processing Systems36\.Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p3.1)\.
- C\. Yang, X\. Wang, Y\. Lu, H\. Liu, Q\. V\. Le, D\. Zhou, and X\. Chen \(2024\)Large language models as optimizers\.InThe Twelfth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=Bb4VGOWELI)Cited by:[Appendix D](https://arxiv.org/html/2606.04661#A4.SS0.SSS0.Px1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p2.1),[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- H\. Yang and K\. Li \(2023\)InstOptima: evolutionary multi\-objective instruction optimization via large language model\-based instruction operators\.InFindings of the Association for Computational Linguistics: EMNLP 2023,H\. Bouamor, J\. Pino, and K\. Bali \(Eds\.\),Singapore,pp\. 13593–13602\.External Links:[Link](https://aclanthology.org/2023.findings-emnlp.907/),[Document](https://dx.doi.org/10.18653/v1/2023.findings-emnlp.907)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- M\. Yue, J\. Zhao, M\. Zhang, L\. Du, and Z\. Yao \(2024\)Large language model cascades with mixture of thought representations for cost\-efficient reasoning\.InThe Twelfth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=6okaSfANzh)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px4.p1.1)\.
- M\. Yuksekgonul, F\. Bianchi, J\. Boen, S\. Liu, P\. Lu, Z\. Huang, C\. Guestrin, and J\. Zou \(2025\)Optimizing generative AI by backpropagating language model feedback\.Nature639,pp\. 609–616\.External Links:[Document](https://dx.doi.org/10.1038/s41586-025-08661-4)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px1.p1.1)\.
- T\. Zehle, M\. Schlager, T\. Heiß, and M\. Feurer \(2025\)CAPO: cost\-aware prompt optimization\.InProceedings of the Fourth International Conference on Automated Machine Learning,L\. Akoglu, C\. Doerr, J\. N\. van Rijn, R\. Garnett, and J\. R\. Gardner \(Eds\.\),Proceedings of Machine Learning Research, Vol\.293,pp\. 18/1–45\.External Links:[Link](https://proceedings.mlr.press/v293/zehle25a.html)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- G\. Zhao, B\. Yoon, G\. Park, S\. Jha, S\. Yoo, and X\. Qian \(2025\)Pareto prompt optimization\.InThe Thirteenth International Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=HGCk5aaSvE)Cited by:[§2](https://arxiv.org/html/2606.04661#S2.SS0.SSS0.Px3.p1.1)\.
- Z\. Zhao, E\. Wallace, S\. Feng, D\. Klein, and S\. Singh \(2021\)Calibrate before use: improving few\-shot performance of language models\.InInternational conference on machine learning,pp\. 12697–12706\.Cited by:[§1](https://arxiv.org/html/2606.04661#S1.p1.1),[§1](https://arxiv.org/html/2606.04661#S1.p3.1)\.
- E\. Zitzler and L\. Thiele \(1999\)Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach\.IEEE transactions on Evolutionary Computation3\(4\),pp\. 257–271\.Cited by:[5th item](https://arxiv.org/html/2606.04661#A2.I1.i5.p1.4),[§4\.4](https://arxiv.org/html/2606.04661#S4.SS4.p1.9)\.

## Appendix AMethod Details

### A\.1Notation

Table[4](https://arxiv.org/html/2606.04661#A1.T4)lists the symbols used in Section[3](https://arxiv.org/html/2606.04661#S3)\.

SymbolDefinitionRRNumber of CRAFT optimization rounds; main experiments useR=8R=8\.TTNumber of validation subsets; conceptually distinct from the optimization\-round countRR, set to88by default\.KclusterK\_\{\\mathrm\{cluster\}\}Number ofkk\-means clusters used to build validation subsets;Kcluster=TK\_\{\\mathrm\{cluster\}\}=T\.kkPopulation size retained by the selector after each round\.nRn\_\{R\}Maximum number of refined candidates generated per round\.nCn\_\{C\}Maximum number of condensed candidates generated per round\.BBUCB\-allocated validation batch size per round; defaultB=2​kB=2k\.μi,t\\mu\_\{i,t\}Running mean validation score for promptPiP\_\{i\}through roundtt; we drop thettsubscript when context fixes the round\.σi,t\\sigma\_\{i,t\}Empirical standard deviation over observed validation scores; conservativeσ=1\\sigma=1floor when\|𝒮i,t\|≤1\|\\mathcal\{S\}\_\{i,t\}\|\\leq 1\.cic\_\{i\}Prompt\-token count ofPiP\_\{i\}\.pi,t\+p^\{\+\}\_\{i,t\}Optimistic scorepi,t\+=μi,t\+βt​σi,tp^\{\+\}\_\{i,t\}=\\mu\_\{i,t\}\+\\beta\_\{t\}\\sigma\_\{i,t\}used for acquisition\.βt\\beta\_\{t\}Linear exploration weight0\.5\+0\.5​max⁡\(0,1−t/R\)0\.5\+0\.5\\max\(0,1\-t/R\), decaying over optimization rounds\.BroundB\_\{\\mathrm\{round\}\}Per\-round LLM\-call budget:k​\(nR\+nC\)k\(n\_\{R\}\+n\_\{C\}\)generation calls plusB⋅\|𝒱π​\(t\)\|B\\cdot\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|validation calls\.𝒫t\\mathcal\{P\}\_\{t\}Retained population of sizekkat roundtt\.𝒬t\\mathcal\{Q\}\_\{t\}Candidate set at roundtt\(refined∪\\cupcondensed∪\\cupretained\)\.𝒱j\\mathcal\{V\}\_\{j\}Thejj\-th validation subset,j∈\{1,…,T\}j\\in\\\{1,\\dots,T\\\}; optimization roundttvalidates on𝒱π​\(t\)\\mathcal\{V\}\_\{\\pi\(t\)\}withπ​\(t\)=\(\(t−1\)modT\)\+1\\pi\(t\)=\(\(t\-1\)\\bmod T\)\+1\.𝒮i,t\\mathcal\{S\}\_\{i,t\}Observation set forPiP\_\{i\}: the validation examples on which it has been scored through roundtt\.𝒜t\\mathcal\{A\}\_\{t\}Archive of all candidates evaluated through roundtt\.ℱt\+\\mathcal\{F\}^\{\+\}\_\{t\}Optimistic Pareto front in\(p~\+,c~\)\(\\tilde\{p\}^\{\+\},\\tilde\{c\}\)space at roundtt\.ℰt\\mathcal\{E\}\_\{t\}Evaluation batch selected at roundtt,\|ℰt\|≤B\|\\mathcal\{E\}\_\{t\}\|\\leq B\.𝒞,𝒞∗\\mathcal\{C\},\\,\\mathcal\{C\}^\{\*\}Generic candidate set and its Pareto\-optimal subset \(Section[3\.1](https://arxiv.org/html/2606.04661#S3.SS1)\)\.Table 4:Notation used in the CRAFT method section\. We use subscripted forms \(μi\\mu\_\{i\},σi\\sigma\_\{i\},cic\_\{i\},pip\_\{i\}\) throughout, adding the round subscripttt\(e\.g\.μi,t\\mu\_\{i,t\},σi,t\\sigma\_\{i,t\},pi,t\+p^\{\+\}\_\{i,t\}\) when a per\-round running estimate is being defined\.
### A\.2Background Primer: NSGA\-II and UCB

This appendix gives the methodological background for the two algorithmic components of CRAFT that are reused from prior work: NSGA\-II selection and UCB acquisition\. Pareto\-front and dominance are defined in Section[3\.1](https://arxiv.org/html/2606.04661#S3.SS1)\(Preliminaries\); hypervolume and IGD are defined in Section[4\.4](https://arxiv.org/html/2606.04661#S4.SS4)and elaborated in Appendix[B\.2](https://arxiv.org/html/2606.04661#A2.SS2)\. Throughout this appendix we use CRAFT’s bi\-objective setting: task scorepi∈\[0,1\]p\_\{i\}\\in\[0,1\]\(maximize\) and prompt\-token costci∈ℤ\>0c\_\{i\}\\in\\mathbb\{Z\}\_\{\>0\}\(minimize\), with the same per\-candidate index convention as in the main paper\.

##### Why a Weighted\-Sum Cannot Replace Front Search\.

A weighted\-sum scalarizationw​p^i\+\(1−w\)​c^iw\\,\\hat\{p\}\_\{i\}\+\(1\-w\)\\,\\hat\{c\}\_\{i\}\(used by our WPRO baselines\) commits to a single tangent of the front, parameterized byww\. It is provably unable to recover non\-convex regions of the Pareto front for any choice ofww\(Das and Dennis,[1997](https://arxiv.org/html/2606.04661#bib.bib258)\): scalarization is fundamentally weaker than direct front search when the trade\-off shape is unknown a priori\. This is the formal statement of the*scalarization\-collapse*failure mode named in Section[1](https://arxiv.org/html/2606.04661#S1)and motivates CRAFT’s front\-aware acquisition\.

#### A\.2\.1Front\-aware selection: non\-dominated sort and maximin spread

CRAFT’s selector reuses fast non\-dominated sort from NSGA\-II\(Debet al\.,[2002](https://arxiv.org/html/2606.04661#bib.bib240)\)and pairs it with a maximin spread tie\-breaker\(Gonzalez,[1985](https://arxiv.org/html/2606.04661#bib.bib262)\)instead of the standard NSGA\-II crowding\-distance estimator\. We describe both ingredients\.

##### Fast Non\-Dominated Sort\.

Given a candidate set of sizeNNwithKKobjectives, the sort partitions candidates into successive Pareto frontsF1,F2,…F\_\{1\},F\_\{2\},\\dots:F1F\_\{1\}contains candidates not dominated by any other,F2F\_\{2\}contains candidates not dominated by any candidate outsideF1F\_\{1\}, and so on\. The procedure runs inO​\(K​N2\)O\(KN^\{2\}\)\.

##### Maximin Spread within a Front\.

Letμ~i\\tilde\{\\mu\}\_\{i\},c~i\\tilde\{c\}\_\{i\}be min\-max normalized estimates in\[0,1\]\[0,1\]\. From the boundary frontFjF\_\{j\}we want to pickm=k−\|𝒫t\|m=k\-\|\\mathcal\{P\}\_\{t\}\|candidates that are spread along the front\. We use the classical farthest\-first traversal\(Gonzalez,[1985](https://arxiv.org/html/2606.04661#bib.bib262)\): seed the selected setSSwith the two extremes ofFjF\_\{j\}\(the candidates that maximizeμ~\\tilde\{\\mu\}and minimizec~\\tilde\{c\}respectively\); then while\|S\|<m\|S\|<m, addi∗=arg​maxi∈Fj∖S⁡mins∈S⁡‖\(μ~i,c~i\)−\(μ~s,c~s\)‖2i^\{\*\}=\\operatorname\*\{arg\\,max\}\_\{i\\in F\_\{j\}\\setminus S\}\\min\_\{s\\in S\}\\\|\(\\tilde\{\\mu\}\_\{i\},\\tilde\{c\}\_\{i\}\)\-\(\\tilde\{\\mu\}\_\{s\},\\tilde\{c\}\_\{s\}\)\\\|\_\{2\}\. Each iteration picks the candidate whose closest neighbor inSSis the farthest away, which spreadsSSas evenly as possible alongFjF\_\{j\}in normalized objective space\. The traversal is seeded from the boundary frontFjF\_\{j\}’s own extremes rather than from the already\-admitted frontsF1,…,Fj−1F\_\{1\},\\dots,F\_\{j\-1\}; this keeps boundary\-front selection self\-contained, at the cost of not explicitly spacing the newly admitted points against the previously retained ones\.

##### Selector\.

To form the next\-round population of sizekk, the selector traversesF1,F2,…F\_\{1\},F\_\{2\},\\dotsin order, admitting whole fronts until the next would overfill\. From the boundary front it picks the remaining candidates by maximin spread, as stated in Algorithm[2](https://arxiv.org/html/2606.04661#alg2)of the main paper\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x7.png)Figure 7:CRAFT selector\. Filled circles are candidates in\(c,μ\)\(c,\\,\\mu\)space; the yellow curve is the non\-dominated front\. Orange\-ringed points are retained by the maximin spread rule; pink dashed\-ring points are on the front but pruned because admitting them would shrink the minimum pairwise distance of the retained set; blue points are dominated\. The rule jointly preserves non\-dominance and even spread\.

#### A\.2\.2Upper\-Confidence\-Bound \(UCB\) acquisition

UCB acquisition is a generic optimism\-under\-uncertainty rule from the bandit literature\(Aueret al\.,[2002](https://arxiv.org/html/2606.04661#bib.bib257); Srinivaset al\.,[2009](https://arxiv.org/html/2606.04661#bib.bib245)\)\. For candidatePiP\_\{i\}with mean estimateμi\\mu\_\{i\}and uncertainty estimateσi\\sigma\_\{i\}, the UCB score isUCBi=μi\+β​σi\\mathrm\{UCB\}\_\{i\}=\\mu\_\{i\}\+\\beta\\sigma\_\{i\}with exploration weightβ\>0\\beta\>0\. Candidates with high mean*or*high uncertainty receive high UCB scores\. As more observations accumulate,σi\\sigma\_\{i\}shrinks and UCB approaches the empirical mean, so confidence intervals tighten with experience\.

The original Gaussian\-process UCB rule\(Srinivaset al\.,[2009](https://arxiv.org/html/2606.04661#bib.bib245)\)derivesσ\\sigmafrom a GP posterior\. CRAFT does not fit a surrogate model over prompts and instead uses an empirical\-SD variant\.σi,t\\sigma\_\{i,t\}is the standard deviation ofPiP\_\{i\}’s per\-example task scores observed so far, with a conservativeσ=1\\sigma=1floor for candidates with≤1\\leq 1observation\. The scheduleβt=0\.5\+0\.5​max⁡\(0,1−t/R\)\\beta\_\{t\}=0\.5\+0\.5\\max\(0,1\-t/R\)starts near11at early rounds and linearly decays to0\.50\.5by the final optimization roundRR, never collapsing to pure exploitation\.

CRAFT’s twist on UCB is multi\-objective\. Instead of one UCB ranking, the optimistic scorespi,t\+=μi,t\+βt​σi,tp^\{\+\}\_\{i,t\}=\\mu\_\{i,t\}\+\\beta\_\{t\}\\sigma\_\{i,t\}are paired with costscic\_\{i\}to form an optimistic front, and the acquisition prefers candidates closest to \(or already on\) that front\. The full rule is in Algorithm[1](https://arxiv.org/html/2606.04661#alg1)\.

##### Mean and Uncertainty\.

For promptPiP\_\{i\}, let𝒮i,t\\mathcal\{S\}\_\{i,t\}be the validation examples on whichPiP\_\{i\}has been evaluated up to roundtt, letz=\(x,y\)z=\(x,y\), andsi​\(z\)=s​\(Pi,x,y\)∈\[0,1\]s\_\{i\}\(z\)=s\(P\_\{i\},x,y\)\\in\[0,1\]the per\-example score\. The running mean and empirical standard deviation are

μi,t\\displaystyle\\mu\_\{i,t\}=1\|𝒮i,t\|​∑z∈𝒮i,tsi​\(z\),\\displaystyle=\\frac\{1\}\{\|\\mathcal\{S\}\_\{i,t\}\|\}\\sum\_\{z\\in\\mathcal\{S\}\_\{i,t\}\}s\_\{i\}\(z\),σi,t\\displaystyle\\sigma\_\{i,t\}=∑z∈𝒮i,t\(si​\(z\)−μi,t\)2max⁡\(\|𝒮i,t\|−1,1\)\.\\displaystyle=\\sqrt\{\\frac\{\\sum\_\{z\\in\\mathcal\{S\}\_\{i,t\}\}\\big\(s\_\{i\}\(z\)\-\\mu\_\{i,t\}\\big\)^\{2\}\}\{\\max\(\|\\mathcal\{S\}\_\{i,t\}\|\-1,\\,1\)\}\}\.With no observations CRAFT setsμi,t=0\\mu\_\{i,t\}=0,σi,t=1\\sigma\_\{i,t\}=1; with one observation it keeps a conservativeσ=1\\sigma=1floor\.

##### Normalized Score\-Cost Coordinates\.

Let𝒜t\\mathcal\{A\}\_\{t\}be the archive of candidates evaluated up to roundtt\. Withpmin\+=minj∈𝒜t⁡pj,t\+,pmax\+=maxj∈𝒜t⁡pj,t\+p^\{\+\}\_\{\\min\}=\\min\_\{j\\in\\mathcal\{A\}\_\{t\}\}p^\{\+\}\_\{j,t\},\\ p^\{\+\}\_\{\\max\}=\\max\_\{j\\in\\mathcal\{A\}\_\{t\}\}p^\{\+\}\_\{j,t\}andcmin=minj∈𝒜t⁡cj,cmax=maxj∈𝒜t⁡cjc\_\{\\min\}=\\min\_\{j\\in\\mathcal\{A\}\_\{t\}\}c\_\{j\},\\ c\_\{\\max\}=\\max\_\{j\\in\\mathcal\{A\}\_\{t\}\}c\_\{j\}, the normalized coordinates are

p~i,t\\displaystyle\\tilde\{p\}\_\{i,t\}=pi,t\+−pmin\+pmax\+−pmin\+\+ϵ,\\displaystyle=\\frac\{p^\{\+\}\_\{i,t\}\-p^\{\+\}\_\{\\min\}\}\{p^\{\+\}\_\{\\max\}\-p^\{\+\}\_\{\\min\}\+\\epsilon\},c~i\\displaystyle\\tilde\{c\}\_\{i\}=ci−cmincmax−cmin\+ϵ,\\displaystyle=\\frac\{c\_\{i\}\-c\_\{\\min\}\}\{c\_\{\\max\}\-c\_\{\\min\}\+\\epsilon\},withϵ\\epsilona small constant to guard against constant archives\. Higherp~\\tilde\{p\}and lowerc~\\tilde\{c\}are preferred\.

##### Complexity\.

Algorithm[1](https://arxiv.org/html/2606.04661#alg1)runs inO​\(\|𝒬t\|​log⁡\|𝒬t\|\)O\(\|\\mathcal\{Q\}\_\{t\}\|\\log\|\\mathcal\{Q\}\_\{t\}\|\)for two\-objective front construction,O​\(\|𝒬t\|⋅\|ℱt\+\|\)O\(\|\\mathcal\{Q\}\_\{t\}\|\\cdot\|\\mathcal\{F\}^\{\+\}\_\{t\}\|\)for per\-candidate gap computation \(bounded byO​\(\|𝒬t\|2\)O\(\|\\mathcal\{Q\}\_\{t\}\|^\{2\}\)in the worst case\), andO​\(\|𝒬t\|​log⁡\|𝒬t\|\)O\(\|\\mathcal\{Q\}\_\{t\}\|\\log\|\\mathcal\{Q\}\_\{t\}\|\)for the final sort\.

##### Pareto Gap\.

For candidateiithe gap to the optimistic frontℱt\+\\mathcal\{F\}^\{\+\}\_\{t\}is

gi=miny∈ℱt\+⁡\[max⁡\(0,p~y,t−p~i,t\)\+max⁡\(0,c~i−c~y\)\]\.g\_\{i\}=\\min\_\{y\\in\\mathcal\{F\}^\{\+\}\_\{t\}\}\\\!\\big\[\\,\\max\(0,\\tilde\{p\}\_\{y,t\}\\\!\-\\\!\\tilde\{p\}\_\{i,t\}\)\+\\max\(0,\\tilde\{c\}\_\{i\}\\\!\-\\\!\\tilde\{c\}\_\{y\}\)\\,\\big\]\.The twomax⁡\(0,⋅\)\\max\(0,\\cdot\)terms count score deficit \(how much lessp~i,t\\tilde\{p\}\_\{i,t\}is than a front point’sp~y,t\\tilde\{p\}\_\{y,t\}\) and cost excess \(how much morec~i\\tilde\{c\}\_\{i\}is than the same front point’sc~y\\tilde\{c\}\_\{y\}\)\. The closest front point in this Manhattan sense determinesgig\_\{i\}\. Geometrically,gi=0g\_\{i\}=0iffPiP\_\{i\}is already non\-dominated in the normalized space\.

### A\.3SCULPT and DISTILL: Module Details

CRAFT’s two candidate generators, SCULPT \(refiner, Section[3\.2](https://arxiv.org/html/2606.04661#S3.SS2)\) and DISTILL \(condenser, Section[3\.3](https://arxiv.org/html/2606.04661#S3.SS3)\), share the critic\-actor scaffold shown in Figure[8](https://arxiv.org/html/2606.04661#A1.F8)\. They differ in the roles assigned to the critic and the actor and in the action sets used \(full details below\)\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x8.png)Figure 8:Shared critic\-actor scaffold for the default refiner \(SCULPT\) and condenser \(DISTILL\) of CRAFT\. The input prompt is parsed into a hierarchical tree; the critic emits feedback to the actor, which applies tree\-level edits to produce a revised prompt\.##### Prompt\-Tree Representation\.

Both modules operate on a hierarchical*prompt tree*: each node is a Heading \(H\), Paragraph \(P\), or List\-item \(L\) with a level, sibling order, GUID, and token count\. The tree is parsed once at the start of each module call\. Nodes are addressed as<NodeType\>\-<Level\>\-<Order\>\-<GUID\>; deleting a node deletes its subtree\.

##### SCULPT Refiner\.

We adapt SCULPT\(Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\)as the default refiner\. The*critic*inspects the parsed prompt tree \(Figure[8](https://arxiv.org/html/2606.04661#A1.F8)\) together with the previous round’s evaluation results, and emits feedback in two channels:*structural feedback*\(reorganization suggestions over the tree such as promote, split, or merge sections\) and*error feedback*\(issues inferred from per\-example predictions vs\. ground truth, such as misclassified examples and ambiguous instructions\)\. The*actor*consumes the redacted tree and the critic’s feedback and outputs a justified sequence of node\-level edits drawn from the action set in Table[5](https://arxiv.org/html/2606.04661#A1.T5)\. Each call returns one revised prompt tree; the actor is callednRn\_\{R\}times per parent per round\.

ActionDescriptionUPDATERewrite a node to clarify instructions, narrow or broaden scope, or fix unclear phrasing\.INSERTAdd a new node \(definition, example, or edge\-case rule\) under a parent\.DELETERemove a redundant, contradictory, or off\-target node and its subtree\.MERGECombine overlapping sibling nodes into one\.REORDERChange sibling order to improve logical flow\.Table 5:Action types in SCULPT for structure\-aware refinement\. Each action operates on the parsed prompt tree of Figure[8](https://arxiv.org/html/2606.04661#A1.F8)\.
##### DISTILL Condenser\.

DISTILL reuses the same critic\-actor scaffold for cost\-oriented edits\. The*critic*receives the token\-annotated prompt tree and a target compression percentage, and emits per\-node feedback respecting four constraints: preserve essential task information, use scoped \(node\-local\) actions, respect tree hierarchy \(deleting a node deletes its subtree\), and meet the target reduction\. The*actor*consumes the critic feedback and applies the action set in Table[6](https://arxiv.org/html/2606.04661#A1.T6)to produce a compressed tree whose token count meets the target\.

ActionDescriptionUpdate NodeReword or simplify a single node\.Update SubtreeSimplify an entire subtree\.Delete NodeRemove redundant sections\.Merge NodesCombine overlapping sibling nodes\.Table 6:Action types in DISTILL for structure\-aware compression\. Each action operates on the parsed prompt tree\.
##### Compression Ratio\.

Per round, DISTILL is callednCn\_\{C\}times with target compression ratios sampled from\[ρmin,ρmax\]\[\\rho\_\{\\min\},\\rho\_\{\\max\}\], where the ratio is the fraction of prompt tokens to remove\. In our experimentsρmin=0\.10\\rho\_\{\\min\}=0\.10,ρmax=0\.20\\rho\_\{\\max\}=0\.20, andnC=4n\_\{C\}=4; the four sampled ratios are passed as inputs to the critic prompt, so the critic emits a per\-node plan that targets each ratio\. The actor enforces the target by adjusting the depth/breadth of deletions and merges\.

##### OPRO Refiner\.

The OPRO refiner variant replaces the SCULPT critic\-actor pair with a single meta\-prompt over the validated history of past prompts\. Its inputs are \(i\) the current promptPiP\_\{i\}and \(ii\) a history block of the top\-kkvalidated past prompts sorted by validation score \(best last\)\. The optimizer LLM is asked to produce one new prompt that scores higher than every prompt in the history block\. We issue the meta\-promptnRn\_\{R\}times per parent with seeded temperature variation and a per\-call distinct\-rewrite instruction, so the LLM producesnRn\_\{R\}different candidates rather than collapsing to a cached response\. OPRO operates on raw prompt text rather than the parsed tree\.

##### EvoPrompt Refiner\.

The EvoPrompt variant replaces the SCULPT critic\-actor pair with a differential\-evolution \(DE\) operator\. Per parent, three validated promptsP1,P2,P3P\_\{1\},P\_\{2\},P\_\{3\}are sampled from the retained population and paired with the parent \(PiP\_\{i\}\)\. The optimizer LLM is asked to \(i\) identify the differences betweenP1P\_\{1\}andP2P\_\{2\}, \(ii\) mutate those differences, \(iii\) combine the mutation withP3P\_\{3\}to produce an intermediate prompt, and \(iv\) cross over the intermediate prompt with the parent to produce the final candidate\. We issue the DE promptnRn\_\{R\}times per parent with different sampled triples\. Like OPRO, EvoPrompt operates on raw prompt text rather than the parsed tree\.

##### Codebase References\.

Full Markdown prompt templates for SCULPT \(structural critic, error critic, actor\), DISTILL \(critic, actor\), OPRO \(meta\-prompt\), and EvoPrompt \(DE operator\), the action\-set implementations, and the prompt\-tree parser are released in the public codebase\.222[https://github\.com/Sshanu/CRAFT/tree/main/src/data/prompt\_enhancer/](https://github.com/Sshanu/CRAFT/tree/main/src/data/prompt_enhancer/)

##### Baseline Construction for DISTILL and LLMLingua\.

All single\-axis baselines run inside the CRAFT loop\. Each round they generatenR\+nCn\_\{R\}\+n\_\{C\}candidates per prompt \(matching CRAFT’s total per\-round generation budget\) from a single module, validate them with the score\-only UCB acquisition rule ofPryzantet al\.\([2023](https://arxiv.org/html/2606.04661#bib.bib15)\)andKumaret al\.\([2025](https://arxiv.org/html/2606.04661#bib.bib234)\), and retain the topkkcandidates by empirical mean task score\. The baselines differ only in the generator: the SCULPT baseline uses the SCULPT refiner; the DISTILL baseline uses the DISTILL condenser; the LLMLingua baseline uses LLMLingua\-2\. All three thus share validation subsets, per\-round budget, acquisition rule, and retention rule with CRAFT, but use one\-axis generation and score\-only ranking\.

##### WPRO Normalization\.

The WPRO baseline scores a candidatePiP\_\{i\}by the weighted sumScore​\(Pi\)=wp​p^i\+wc​c^i\\mathrm\{Score\}\(P\_\{i\}\)=w\_\{p\}\\hat\{p\}\_\{i\}\+w\_\{c\}\\hat\{c\}\_\{i\}, wherep^i\\hat\{p\}\_\{i\}andc^i\\hat\{c\}\_\{i\}are the min\-max\-normalized accuracy and token reduction over the current candidate set:

p^i\\displaystyle\\hat\{p\}\_\{i\}=μi−minj⁡μjmaxj⁡μj−minj⁡μj,\\displaystyle=\\frac\{\\mu\_\{i\}\-\\min\_\{j\}\\mu\_\{j\}\}\{\\max\_\{j\}\\mu\_\{j\}\-\\min\_\{j\}\\mu\_\{j\}\},c^i\\displaystyle\\hat\{c\}\_\{i\}=maxj⁡cj−cimaxj⁡cj−minj⁡cj\.\\displaystyle=\\frac\{\\max\_\{j\}c\_\{j\}\-c\_\{i\}\}\{\\max\_\{j\}c\_\{j\}\-\\min\_\{j\}c\_\{j\}\}\.Both lie in\[0,1\]\[0,1\], with larger values denoting higher accuracy and greater token reduction respectively\.

### A\.4Validation Subset Construction Detail

This appendix expands the one\-paragraph description of validation subsets in Section[3\.4](https://arxiv.org/html/2606.04661#S3.SS4)\.

##### Why Partial Validation\.

A full\-validation round would evaluate every selected candidate on allNvalN\_\{\\mathrm\{val\}\}examples in𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}\. WithBBcandidates evaluated per round acrossRRrounds, the total validation\-call count would beR⋅B⋅NvalR\\cdot B\\cdot N\_\{\\mathrm\{val\}\}\. Partial validation replacesNvalN\_\{\\mathrm\{val\}\}with\|𝒱π​\(t\)\|\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|per round, cutting cost by a factor ofNval/\|𝒱π​\(t\)\|N\_\{\\mathrm\{val\}\}/\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|\. In the main experiments,T=8T=8,R=8R=8,B=2​k=8B=2k=8, andNvalN\_\{\\mathrm\{val\}\}is taken from Table[7](https://arxiv.org/html/2606.04661#A2.T7); this saves a factor ofT=8T=8in validation calls\.

##### Why Clustered Subsets\.

𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}is partitioned intoTTclusters bykk\-means\(MacQueen,[1967](https://arxiv.org/html/2606.04661#bib.bib256)\)in embedding space, usingall\-MiniLM\-L6\-v2sentence embeddings\(Reimers and Gurevych,[2019](https://arxiv.org/html/2606.04661#bib.bib159)\)\. Each cluster becomes one validation subset𝒱j\\mathcal\{V\}\_\{j\},j∈\{1,…,T\}j\\in\\\{1,\\dots,T\\\}\. Compared with random sampling, clustered subsets give each round semantically coherent examples; this avoids the variance from random sampling, where one round’s subset can be substantially easier than another’s by chance\. The trade\-off is that any per\-subset evaluation depends on the cluster’s idiosyncrasies; this is mitigated because the running meanμi,t\\mu\_\{i,t\}accumulates evidence across the subsets wherePiP\_\{i\}has been evaluated\.

##### Embedding\-Model Choice\.

all\-MiniLM\-L6\-v2is a 22M\-parameter sentence transformer trained for general semantic similarity\. It is small enough that the embedding step is negligible compared to LLM calls and gives meaningful clusters for short classification and reasoning inputs\. We did not sweep across embedding models; this is flagged as a limitation \(Section[7](https://arxiv.org/html/2606.04661#S7)\)\.

##### Subset Rotation and Cumulative Observations\.

The validation subset used at optimization roundttis𝒱π​\(t\)\\mathcal\{V\}\_\{\\pi\(t\)\}withπ​\(t\)=\(\(t−1\)modT\)\+1\\pi\(t\)=\(\(t\-1\)\\bmod T\)\+1\(1\-indexed\); withT=8T=8and the main\-experimentR=8R=8, the evaluator visits each subset exactly once across the run, and diagnostic runs withR\>TR\>Trevisit subsets cyclically\. For a candidatePiP\_\{i\}that is retained across multiple rounds, the observation set𝒮i,t\\mathcal\{S\}\_\{i,t\}is the union of all𝒱π​\(τ\)\\mathcal\{V\}\_\{\\pi\(\\tau\)\}on whichPiP\_\{i\}has been evaluated through roundtt\. The running meanμi,t\\mu\_\{i,t\}averages over𝒮i,t\\mathcal\{S\}\_\{i,t\}, and the empirical standard deviationσi,t\\sigma\_\{i,t\}uses the same per\-example scores\. As a result, long\-lived candidates accumulate evidence across multiple subsets, and\|𝒮i,t\|\|\\mathcal\{S\}\_\{i,t\}\|can exceed\|𝒱π​\(t\)\|\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|\.

##### Initial\-Round Special Case\.

Before the first optimization round, the evaluator measures the initial prompt’s full validation scoreμ0,0\\mu\_\{0,0\}on all of𝒟val\\mathcal\{D\}\_\{\\mathrm\{val\}\}rather than on a single subset𝒱j\\mathcal\{V\}\_\{j\}\. This avoids using a single\-cluster subset to set the reference for subsequent feasibility checks \(the0\.95⋅pinit0\.95\\cdot p\_\{\\mathrm\{init\}\}threshold in Section[4\.4](https://arxiv.org/html/2606.04661#S4.SS4)\)\.

### A\.5Batch\-Relative Candidate Pruning

Between validation and selection, CRAFT prunes candidates that are consistently weak relative to the current round’s batch, so later rounds are not spent re\-exploring them\. The rule is batch\-relative and uncertainty\-aware, and is deliberately lenient: it is*not*the strict0\.95​pinit0\.95\\,p\_\{\\mathrm\{init\}\}feasibility filter used for reporting \(Section[4\.4](https://arxiv.org/html/2606.04661#S4.SS4)\), so moderately weak prompts that may recover in later rounds are retained\.

For each validated candidatePiP\_\{i\}we form a lower\-confidence\-bound scoreℓi=μi,t−βt​σi,t\\ell\_\{i\}=\\mu\_\{i,t\}\-\\beta\_\{t\}\\sigma\_\{i,t\}\. A single strictness knobf∈\[0,1\]f\\in\[0,1\]\(set tof=0\.7f=0\.7in all runs\) maps to a quantileqqand a marginδ\\delta:

q\\displaystyle q=qmin\+\(qmax−qmin\)​f,\\displaystyle=q\_\{\\min\}\+\(q\_\{\\max\}\-q\_\{\\min\}\)\\,f,δ\\displaystyle\\delta=δmax−\(δmax−δmin\)​f,\\displaystyle=\\delta\_\{\\max\}\-\(\\delta\_\{\\max\}\-\\delta\_\{\\min\}\)\\,f,with\(qmin,qmax\)=\(0\.70,0\.98\)\(q\_\{\\min\},q\_\{\\max\}\)=\(0\.70,0\.98\)and\(δmin,δmax\)=\(0\.05,0\.15\)\(\\delta\_\{\\min\},\\delta\_\{\\max\}\)=\(0\.05,0\.15\); atf=0\.7f=0\.7this givesq≈0\.90q\\approx 0\.90andδ≈0\.08\\delta\\approx 0\.08\. The pruning threshold blends the batchqq\-quantile with a margin below the batch maximum,

τ=12​\(quantileq​\(\{ℓi\}\)\+\(maxi⁡ℓi−δ\)\),\\tau=\\tfrac\{1\}\{2\}\\big\(\\mathrm\{quantile\}\_\{q\}\(\\\{\\ell\_\{i\}\\\}\)\+\(\\textstyle\\max\_\{i\}\\ell\_\{i\}\-\\delta\)\\big\),and candidates withℓi≥τ\\ell\_\{i\}\\geq\\tauare kept\. A floor of⌈1\.5​k⌉\\lceil 1\.5\\,k\\rceilcandidates is always retained: if fewer pass, the top\-⌈1\.5​k⌉\\lceil 1\.5\\,k\\rceilbyℓi\\ell\_\{i\}are kept instead\. Becauseτ\\tauis defined from the batch, the rule adapts to each round’s score distribution rather than imposing an absolute cutoff\.

## Appendix BExperimental Setup

### B\.1Dataset Statistics

Table[7](https://arxiv.org/html/2606.04661#A2.T7)reports the validation/test split sizes used in our experiments\. For BeaverTails and GoEmotions we cap the public splits at 200 and 500 examples respectively to keep validation cost comparable across datasets\. For the four BIG\-Bench Hard tasks the public splits are smaller than this cap, so the cap is non\-binding and the counts shown are the dataset’s own validation/test sizes\.

Abbr\.DatasetNvalN\_\{\\mathrm\{val\}\}NtestN\_\{\\mathrm\{test\}\}Task scoreBTBeaverTails200500weighted\-F1GoEGoEmotions200500micro\-F1DQADisambiguationQA50175exact acc\.CJCausal Judgement37130macro\-F1FFFormal Fallacies50175macro\-F1STSalient Translation50175macro\-F1Table 7:Validation/test split sizes per dataset, with the task\-score definition used in our experiments\. Counts reflect the smaller of \(i\) the dataset’s public split and \(ii\) the 200/500 cap we apply uniformly across datasets\.##### BeaverTails \(BT\)\.

A multi\-class safety classification dataset of human\-LLM dialogues\(Jiet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib228)\); each prompt\-response pair carries 14 binary harm\-category labels \(e\.g\.,*discrimination, hate speech*,*drug abuse*,*financial crime*\)\. We score with weighted\-F1 across the 14 labels\.

##### GoEmotions \(GoE\)\.

A 27\-emotion classification dataset of English Reddit comments\(Demszkyet al\.,[2020](https://arxiv.org/html/2606.04661#bib.bib227)\)including categories like*joy, sadness, gratitude, anger, neutral*\. Multi\-label; we score with micro\-F1\.

##### DisambiguationQA \(DQA\)\.

A BIG\-Bench Hard task\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)in which the model resolves a pronoun in a short sentence to its correct antecedent \(often a gender\-disambiguation example\)\. Single\-answer multiple choice; scored with exact accuracy\.

##### Causal Judgement \(CJ\)\.

A BIG\-Bench Hard task\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)that asks the model to judge whether one event causally explains another in a short paragraph; binary answer scored with macro\-F1\.

##### Formal Fallacies \(FF\)\.

A BIG\-Bench Hard task\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)that asks whether a short argument is a syntactically valid deductive inference; binary answer scored with macro\-F1\.

##### Salient Translation Error Detection \(ST\)\.

A BIG\-Bench Hard task\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)that asks the model to identify which of six error categories \(e\.g\.,*named\-entity, numeric, modifiers\-adjectives*\) best describes a translation mistake; six\-way classification scored with macro\-F1\.

### B\.2Evaluation Metrics: Full Definitions

This appendix expands Section[4\.4](https://arxiv.org/html/2606.04661#S4.SS4)\. All metrics are computed on the final retained population at the chosen round snapshot\.

##### Feasibility Filter\.

A prompt is*feasible*if its test score is at least0\.95×0\.95\\timesthe initial\-prompt test score\. Cost\-leaning metrics \(min feasible tokens, peak efficiency\) are computed only over the feasible subset to prevent rewarding degenerate prompts that are short only because they fail the task\.

##### Per\-Metric Definitions\.

- •Best score:maxi⁡pi\\max\_\{i\}p\_\{i\}across thekkretained candidates\.
- •Mean retained\-population score\(Meanin tables and figures\):\(1/k\)​∑i∈𝒫tpi\(1/k\)\\sum\_\{i\\in\\mathcal\{P\}\_\{t\}\}p\_\{i\}across the retained set𝒫t\\mathcal\{P\}\_\{t\}\.
- •Min feasible tokens:mini⁡ci\\min\_\{i\}c\_\{i\}across feasible candidates only\.
- •Peak efficiency\(Eff =EmaxE\_\{\\max\}\):100⋅maxi⁡pi/ci100\\cdot\\max\_\{i\}p\_\{i\}/c\_\{i\}across feasible candidates, reported in percent\-score\-points per 100 tokens \(matching the main\-text definition in §[4\.4](https://arxiv.org/html/2606.04661#S4.SS4)\)\.
- •Hypervolume\(HV\)\(Zitzler and Thiele,[1999](https://arxiv.org/html/2606.04661#bib.bib250)\): the area of the\(p,c\)\(p,c\)\-plane dominated by the retained front, measured against a fixed worst\-corner reference point at zero accuracy and a deliberately large token count \(r=\(0,cref\)r=\(0,\\,c\_\{\\mathrm\{ref\}\}\)withcref=100000c\_\{\\mathrm\{ref\}\}=100000\)\. This reference acts as the origin of the dominated\-volume calculation: higher tokens \(worse cost\) sit at the origin, so retained prompts at lower cost and higher accuracy contribute more area\. The reference is chosen far beyond any prompt observed in our runs so every retained candidate contributes positively\. Reported HV is the raw value normalized to the initial\-prompt corner\(pinit,cinit\)\(p\_\{\\mathrm\{init\}\},c\_\{\\mathrm\{init\}\}\), making HV comparable within a dataset across methods; we do*not*compare HV across datasets because the references differ\.
- •Inverted Generational Distance\(IGD\)\(Bosman and Thierens,[2003](https://arxiv.org/html/2606.04661#bib.bib255)\):IGD​\(F;F∗\)=\(1/\|F∗\|\)​∑q∈F∗minp∈F⁡d​\(q,p\)\\mathrm\{IGD\}\(F;F^\{\*\}\)=\(1/\|F^\{\*\}\|\)\\sum\_\{q\\in F^\{\*\}\}\\min\_\{p\\in F\}d\(q,p\), whereddis Euclidean distance in min\-max normalized\(p~,c~\)\(\\tilde\{p\},\\tilde\{c\}\)coordinates\. Classical IGD uses an externally known true front; for each dataset we substitute the union of all methods’ feasible fronts asF∗F^\{\*\}, since no externally validated Pareto front is available for prompt search\. IGD penalizes fronts that leave regions ofF∗F^\{\*\}uncovered, complementing HV which rewards dominated area\.
- •Front size\(\|ℱ\|\|\\mathcal\{F\}\|\): the cardinality of the final non\-dominated set\. Reported for continuity with prior multi\-objective evolutionary algorithm \(MOEA\) work, but it is bounded bykk\.

##### Composite Rank\.

For each metricxxand datasetddwe rank the compared methods from 1 to\|M\|\|M\|\(1 is best\)\. The composite first averages ranks within each aspect group \(front quality𝒜q\\mathcal\{A\}\_\{\\mathrm\{q\}\}, score𝒜s\\mathcal\{A\}\_\{\\mathrm\{s\}\}, cost𝒜c\\mathcal\{A\}\_\{\\mathrm\{c\}\}\), then averages across the three groups and across datasets\. As a worked example, CRAFT’s per\-metric mean ranks, read from Figure[4](https://arxiv.org/html/2606.04661#S4.F4), are HV 2\.33,\|ℱ\|\|\\mathcal\{F\}\|2\.83, IGD 2\.50 \(sor𝒜q=2\.55r\_\{\\mathcal\{A\}\_\{\\mathrm\{q\}\}\}=2\.55\); best 2\.25, mean 2\.50 \(sor𝒜s=2\.375r\_\{\\mathcal\{A\}\_\{\\mathrm\{s\}\}\}=2\.375\); peak efficiency 3\.67, min feasible tokens 3\.83 \(sor𝒜c=3\.75r\_\{\\mathcal\{A\}\_\{\\mathrm\{c\}\}\}=3\.75\)\. The composite is the mean across aspects:\(2\.55\+2\.375\+3\.75\)/3=2\.89\(2\.55\+2\.375\+3\.75\)/3=2\.89\.

## Appendix CAdditional Results

### C\.1Full Per\-Dataset Results

Table[8](https://arxiv.org/html/2606.04661#A3.T8)reports the full per\-dataset metrics that back the rank\-based comparisons in §[5](https://arxiv.org/html/2606.04661#S5)\.

BTMethodBest↑\\uparrowMean↑\\uparrowTok↓\\downarrowEff↑\\uparrowHV↑\\uparrowIGD↓\\downarrow\|ℱ\|\|\\mathcal\{F\}\|↑\\uparrowInitial54\.054\.06078\.9n/an/a1WPRO0\.356\.055\.823923\.454k0\.462WPRO0\.557\.557\.229619\.457k0\.472WPRO0\.761\.560\.141914\.758k0\.292SCULPT61\.060\.51,6073\.860k0\.752DISTILL55\.055\.035015\.755k0\.452LLMLingua55\.055\.049711\.152k0\.461CRAFT62\.061\.361310\.161k0\.552GoEInitial34\.034\.07944\.3n/an/a1WPRO0\.331\.531\.5∞\\infty∞\\infty31k0\.702WPRO0\.543\.040\.08565\.040k0\.122WPRO0\.739\.539\.28454\.738k0\.392SCULPT37\.036\.02,5901\.435k0\.842DISTILL33\.033\.03898\.532k0\.421LLMLingua34\.033\.05815\.933k0\.342CRAFT37\.535\.54847\.736k0\.232DQAInitial76\.676\.651215\.0n/an/a1WPRO0\.373\.770\.519038\.874k0\.412WPRO0\.576\.073\.625130\.372k0\.473WPRO0\.770\.368\.522830\.870k0\.652SCULPT82\.381\.11,2406\.678k0\.522DISTILL76\.674\.622434\.273k0\.412LLMLingua76\.074\.629825\.575k0\.403CRAFT77\.775\.122534\.577k0\.203
CJMethodBest↑\\uparrowMean↑\\uparrowTok↓\\downarrowEff↑\\uparrowHV↑\\uparrowIGD↓\\downarrow\|ℱ\|\|\\mathcal\{F\}\|↑\\uparrowInitial68\.568\.549913\.7n/an/a1WPRO0\.365\.564\.510363\.665k0\.682WPRO0\.563\.162\.0∞\\infty∞\\infty62k0\.782WPRO0\.774\.273\.268210\.973k0\.302SCULPT76\.972\.71,7844\.375k0\.374DISTILL68\.568\.514048\.963k0\.471LLMLingua65\.265\.1∞\\infty∞\\infty65k0\.621CRAFT74\.271\.235121\.173k0\.302FFInitial71\.871\.852613\.7n/an/a1WPRO0\.379\.777\.416149\.578k0\.322WPRO0\.580\.780\.320439\.674k0\.442WPRO0\.774\.773\.220636\.374k0\.532SCULPT73\.972\.21,2196\.169k1\.061DISTILL91\.490\.219846\.285k0\.252LLMLingua98\.998\.925438\.992k0\.461CRAFT90\.487\.524536\.980k0\.392STInitial62\.162\.141914\.8n/an/a1WPRO0\.360\.459\.78273\.757k0\.492WPRO0\.561\.859\.59863\.158k0\.442WPRO0\.767\.066\.023828\.160k0\.342SCULPT71\.771\.71,2905\.670k0\.852DISTILL61\.260\.914941\.161k0\.462LLMLingua60\.059\.041914\.360k0\.562CRAFT68\.467\.719036\.067k0\.342

Table 8:Main GPT\-5 comparison atR=8R=8across the six datasets \(left: BT, GoE, DQA; right: CJ, FF, ST\)\. Bold marks the best per \(dataset, column\); lower is better for Tok and IGD, higher otherwise\. “n/a” on the initial\-prompt row marks HV and IGD that are undefined for a single point\. “∞\\infty” marks rows where no retained prompt clears the feasibility filter \(p≥0\.95​pinitp\\geq 0\.95\\,p\_\{\\mathrm\{init\}\}\); the marker applies to both Tok and Eff, which share the feasibility filter and are therefore both undefined in that case\. Values averaged across two seeds\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x9.png)Figure 9:Per\-dataset composite rank atR=8R=8\(rank↓\\downarrow\)\. CRAFT leads DQA and ST; WPRO0\.5leads BT and GoE; SCULPT leads CJ; DISTILL leads FF\.##### Per\-Dataset Detail\.

Across the six datasets, CRAFT places 1st on DQA and ST, 2nd on CJ \(tied with WPRO0\.7\) and GoE, 3rd on BT \(within0\.110\.11of the leader WPRO0\.5\), and 4th on FF\. No other method matches this consistency: SCULPT reaches rank6\.946\.94on FF, WPRO0\.3reaches6\.726\.72on GoE, WPRO0\.7reaches6\.066\.06on DQA, WPRO0\.5reaches6\.286\.28on CJ, and LLMLingua reaches5\.895\.89on ST\. CRAFT is the only method whose worst\-case per\-dataset rank stays below 4 \(at3\.723\.72on FF\), reflecting robustness across the front\-quality, score, and cost aspects rather than dominance on individual datasets\.

### C\.2Per\-Dataset Optimization Dynamics

Figures[10](https://arxiv.org/html/2606.04661#A3.F10)to[15](https://arxiv.org/html/2606.04661#A3.F15)report the per\-round dynamics view \(hypervolume, min feasible tokens, best score, peak efficiency\) for all six GPT 5 benchmarks, capped at the defaultR=8R=8snapshot\. Gaps in the \(b\) Min feasible tokens curve mark rounds where no DISTILL candidate passed the feasibility filter \(p≥0\.95​pinitp\\geq 0\.95\\,p\_\{\\mathrm\{init\}\}\); the other curves plot directly from each method’s per\-round Pareto report\.

![Refer to caption](https://arxiv.org/html/2606.04661v1/x10.png)Figure 10:Optimization dynamics on BT \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x11.png)Figure 11:Optimization dynamics on GoE \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x12.png)Figure 12:Optimization dynamics on DQA \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x13.png)Figure 13:Optimization dynamics on CJ \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x14.png)Figure 14:Optimization dynamics on FF \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.![Refer to caption](https://arxiv.org/html/2606.04661v1/x15.png)Figure 15:Optimization dynamics on ST \(GPT\-5\) over rounds 0 to 8 for CRAFT, SCULPT, and DISTILL: \(a\) hypervolume, \(b\) min feasible tokens, \(c\) best score, \(d\) peak efficiency\.

## Appendix DArtifacts, Reproducibility, and Responsible Use

##### Datasets, Models, and Code\.

We evaluate on six public benchmarks: BeaverTails\(Jiet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib228)\), GoEmotions\(Demszkyet al\.,[2020](https://arxiv.org/html/2606.04661#bib.bib227)\), and four BIG\-Bench Hard tasks\(Suzgunet al\.,[2023](https://arxiv.org/html/2606.04661#bib.bib219)\)\(Disambiguation QA, Causal Judgement, Formal Fallacies, and Salient Translation Error Detection\)\. The optimizer and target models are hosted LLMs: the GPT\-5 family\(Singhet al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib215)\), DeepSeek\-V4 Flash\(DeepSeek\-AI,[2026](https://arxiv.org/html/2606.04661#bib.bib217)\), and Kimi\-K2\.5\(Teamet al\.,[2026](https://arxiv.org/html/2606.04661#bib.bib216)\)\. The refiner and condenser build on SCULPT\(Kumaret al\.,[2025](https://arxiv.org/html/2606.04661#bib.bib234)\); baselines additionally use OPRO\(Yanget al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib9)\), EvoPrompt\(Guoet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib19)\), and LLMLingua\-2\(Panet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib230)\)\. Every dataset, model, and baseline method is cited at first use\. All six datasets are public research benchmarks for text classification or reasoning, and we use each only to evaluate prompt optimization, consistent with its intended research use\.

##### Licenses\.

The datasets are distributed for research use: BeaverTails under CC BY\-NC 4\.0, GoEmotions under Apache\-2\.0, and BIG\-Bench Hard under the MIT license\. Our use is non\-commercial academic research and falls within these terms\. The hosted LLMs are accessed through their providers’ inference APIs under the respective API terms of service\.

##### Computational Budget and Infrastructure\.

All experiments run through hosted LLM inference APIs; we train no model, so no GPU hours are consumed, and parameter counts for the API models are not publicly disclosed by their providers\. The dominant cost is the number of LLM calls\. Each round, CRAFT issuesk​\(nR\+nC\)=48k\(n\_\{R\}\+n\_\{C\}\)=48candidate\-generation calls andB⋅\|𝒱π​\(t\)\|B\\cdot\|\\mathcal\{V\}\_\{\\pi\(t\)\}\|validation calls, with validation\-subset sizes following Table[7](https://arxiv.org/html/2606.04661#A2.T7), repeated overR=8R=8rounds; the same per\-round call budget applies to every compared method \(§[4](https://arxiv.org/html/2606.04661#S4)\)\. Sentence\-embedding andkk\-means clustering for the validation subsets run once per dataset on CPU and are negligible next to the LLM calls\.

##### Software and Package Settings\.

The implementation is in Python\. LLM calls are issued through the officialopenaiandazure\-ai\-inferenceclient libraries, and runs are configured with Hydra and OmegaConf\. Prompt\-token costc​\(P\)c\(P\)is measured with thetiktokentokenizer, and prompts are parsed and edited as trees withnetworkx\. Validation subsets are constructed withkk\-means clustering\(MacQueen,[1967](https://arxiv.org/html/2606.04661#bib.bib256)\)fromscikit\-learn, overall\-MiniLM\-L6\-v2sentence embeddings\(Reimers and Gurevych,[2019](https://arxiv.org/html/2606.04661#bib.bib159)\)produced bysentence\-transformerson a PyTorch backend, usingT=8T=8clusters\. The LLMLingua\-2 baseline uses thellmlinguapackage\(Panet al\.,[2024](https://arxiv.org/html/2606.04661#bib.bib230)\)with its default token\-level compression configuration\. Numerical routines usenumpy,scipy, andpandas\. All LLM calls fix the generation temperature to0\(§[4](https://arxiv.org/html/2606.04661#S4)\)\. A full dependency list will be released with the code\.

##### Potential Risks\.

CRAFT optimizes whatever task score it is given\. If that score rewards adversarial behavior \(for example, eliciting unsafe outputs from the target LLM\), the same loop that finds high\-accuracy, low\-cost prompts can also produce shorter and more reliable jailbreak prompts\. Mitigation is the responsibility of whoever defines the task score; CRAFT itself adds no safety constraints beyond those of the target LLM\.