# Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction

arXiv: https://arxiv.org/abs/1310.0732 · HTML: https://mlsanity.com/paper/1310.0732/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2013.

## Built on by (most cited first, 21 of 21)

- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05944/) (2022)
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- [Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.06980/) (2021)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL](https://mlsanity.com/paper/2505.21974/) (2025)
- [A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization](https://mlsanity.com/paper/2206.11526/) (2022)
- [Fantasizing with Dual GPs in Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2211.01053/) (2022)
- [Combined Global and Local Search for Optimization with Gaussian Process Models](https://mlsanity.com/paper/2107.03217/) (2021)
- [Regularized infill criteria for multi-objective Bayesian optimization with application to aircraft design](https://mlsanity.com/paper/2504.08671/) (2025)
- [Multi-objective optimisation via the R2 utilities](https://mlsanity.com/paper/2305.11774/) (2023)
- [Pareto-frontier Entropy Search with Variational Lower Bound Maximization](https://mlsanity.com/paper/2501.19073/) (2025)
- [Choice functions based multi-objective Bayesian optimisation](https://mlsanity.com/paper/2110.08217/) (2021)
- [Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds](https://mlsanity.com/paper/2506.21887/) (2025)
- [One Step Preference Elicitation in Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2105.13278/) (2021)
- [Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method](https://mlsanity.com/paper/2207.03842/) (2022)
- [Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modeling](https://mlsanity.com/paper/2511.09598/) (2025)
- [Collaborative Multidisciplinary Design Optimization with Neural Networks](https://mlsanity.com/paper/2106.06092/) (2021)
- [Multi-objective robust optimization using adaptive surrogate models for problems with mixed continuous-categorical parameters](https://mlsanity.com/paper/2203.01996/) (2022)
- [Vector Optimization with Gaussian Process Bandits](https://mlsanity.com/paper/2412.02484/) (2024)
- [Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties](https://mlsanity.com/paper/2609.19858/) (2026)

## Abstract (arXiv)

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We present here a new algorithm based on stepwise uncertainty reduction principles to address this issue. Optimization is seen as a sequential reduction of the volume of the excursion sets below the current best solutions, and our sampling strategy chooses the points that give the highest expected reduction. Closed-form formulae are provided to compute the sampling criterion, avoiding the use of cumbersome simulations. We test our method on numerical examples, showing that it provides an efficient trade-off between exploration and intensification.