# Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties

arXiv: https://arxiv.org/abs/2609.19858 · HTML: https://mlsanity.com/paper/2609.19858/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework](https://mlsanity.com/paper/1904.08823/) (2019)
- [Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing](https://mlsanity.com/paper/2004.05068/) (2020)
- [Random Pareto front surfaces](https://mlsanity.com/paper/2405.01404/) (2024)
- [Multiobjective Optimization under Uncertainties using Conditional Pareto Fronts](https://mlsanity.com/paper/2504.04944/) (2025)
- [Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation](https://mlsanity.com/paper/2511.12545/) (2025)

## Abstract (arXiv)

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.