Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties

arXiv cs.LG Papers
multiobjective-optimization uncertainties hypervolume gaussian-processes active-learning

Summary

This paper proposes a Bayesian decision formulation for multiobjective optimization under uncertainties, emphasizing expected hypervolume maximization with Gaussian Processes and active learning strategies.

arXiv:2609.19858v1 Announce Type: new Abstract: The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.
Original Article
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# Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties
Source: [https://arxiv.org/abs/2609.19858](https://arxiv.org/abs/2609.19858)
Authors:[Victor Trappler](https://arxiv.org/search/cs?searchtype=author&query=Trappler,+V)\(Mines Saint\-Étienne MSE, LIMOS, FAYOL\-ENSMSE, FAYOL\-ENSMSE\)

[View PDF](https://arxiv.org/pdf/2609.19858)

> Abstract:The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective\. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points\. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points\. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization\. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well\-designed for the multiobjective optimization problem at stake\. These strategies are compared on simple analytical problems to assess their performances\.

## Submission history

From: Victor Trappler \[[view email](https://arxiv.org/show-email/9f5da856/2609.19858)\] \[via CCSD proxy\] **\[v1\]**Thu, 17 Sep 2026 08:10:15 UTC \(7,357 KB\)

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