convex-optimization

该论文确定了在重尾噪声（有界中心 p 阶矩，1<p≤2）下，平滑凸目标的裁剪 SGD 最后一次迭代的时间一致（time-uniform）最优收敛速率，证明了无需已知时间跨度的调度可达 O~(t^{-2(p-1)/(3p-1)})，且不存在更优的规则，回答了未知停止时间对收敛的代价问题。

该论文刻画了在线凸优化中仅能访问线性优化预言机时的紧确遗憾界，给出了维度无关的极小极大期望遗憾 Θ(GD·max{√T, T/(1+min{Q,BT})^{1/4}})，并同时证明了适用于任意随机化学习者的下界与匹配的算法上界。

This paper proposes a meta-learning framework for online convex optimization with indicator switching costs, achieving minimax-optimal dynamic regret bounds without prior knowledge of comparator variations.

This paper proposes a tail-aware geometry learning framework for conformal ellipsoids that decouples tail sensitivity from coverage guarantees, improving uncertainty quantification in multivariate settings.

This paper proposes a regularized least squares training approach for quadratic neural networks, providing closed-form expressions for weights and sensitivity, with applications to system identification.

This paper extends CONES to time-varying loss functions, showing bounds for regret and movement cost using projected proximal algorithms in convex optimization.

This paper proves that Thompson sampling achieves polynomial regret for non-monotone convex ridge bandits, showing that monotonicity is not necessary, with a new regret bound of Õ(d^{9/2} √n).

This paper revisits median-of-means estimation from a deterministic optimization perspective and develops a family of block-Lp estimators for robust learning under heavy-tailed and adversarial corruption, showing that nonconvex methods can approach the trimmed oracle performance while remaining computationally tractable.

This paper introduces a post-generation guardrail pipeline for LLMs in financial portfolio advice, using convex projection to enforce KYC constraints and reduce feasibility violations to 0% with minimal correction.

The article discusses the impact of Stephen Boyd's 2006 mathematics textbook on convex optimization, used by Google, Renaissance Technologies, and others, and promotes his free Stanford course EE364A available on YouTube.

This paper proposes a provable two-stage pipeline that distills nonlinear dynamical systems into compact linear state-space models using convex optimization, with theoretical guarantees and experiments on LDS benchmarks and MuJoCo.

This theoretical paper studies the non-asymptotic implicit bias of logistic regression under gradient descent, proving that the parameter vector weakly aligns with the max-margin direction quickly, within a doubly exponential number of iterations in the alignment error.

DecoupleMix introduces a systematic framework for optimizing pretraining data mixtures for Vision-Language Models by decoupling inter-class and intra-class ratio search, using convex optimization to improve scalability and performance over heuristic baselines.

This paper analyzes the scaling limits of constant-stepsize SGD near flat minima, showing that the invariant law concentrates at scale α^(1/m) for objectives with flatness exponent m ≥ 2, and converges to non-Gaussian stationary distributions for m > 2.

Following OpenAI's CDC proof announcement, GPT-5.6 reportedly solved a 30-year open problem in convex optimization using a similar prompt, with the solution verified in the Lean proof assistant.

GPT-5.6 significantly outperforms published state-of-the-art on a fundamental mathematical problem about gradient flow length, achieving exponential improvements. This marks a major advance in AI's ability to reason about complex mathematical questions.

A tweet highlights Stanford professor Stephen Boyd's free convex optimization course and textbook, noting that Citadel pays $400K for this skill. The course teaches optimal portfolio allocation, but emphasizes that the optimizer only works with a genuine edge in signals.

Introduces Simplex-Constrained Sparse Bagging (SCSB), a post-training framework that optimizes estimator weights over the probability simplex using out-of-bag samples, achieving up to 96% ensemble compression and improved calibration.

This paper reveals that Mirror Descent with non-quadratic regularizers can be exponentially more sensitive to initialization than Gradient Descent, even under well-conditioned settings, which has implications for reproducibility in RL and LLM post-training.

This paper introduces a curvature-adaptive Follow-the-Perturbed-Leader (FTPL) algorithm for online optimization that achieves optimal regret bounds for both non-convex Lipschitz losses and strongly convex losses, using a time-varying perturbation scale.