# Predictive Entropy Search for Multi-objective Bayesian Optimization

arXiv: https://arxiv.org/abs/1511.05467 · HTML: https://mlsanity.com/paper/1511.05467/

## Key facts

- Cited by 88 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2015.

## Built on by (most cited first, 30 of 88)

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- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [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)
- [Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview](https://mlsanity.com/paper/2206.07438/) (2022)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [BORE: Bayesian Optimization by Density-Ratio Estimation](https://mlsanity.com/paper/2102.09009/) (2021)
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- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
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- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
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- [Multi-Objective Bayesian Optimization with Active Preference Learning](https://mlsanity.com/paper/2311.13460/) (2023)
- [Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.08799/) (2024)
- [Vector Optimization with Stochastic Bandit Feedback](https://mlsanity.com/paper/2110.12311/) (2021)
- [Unicorn: Reasoning about Configurable System Performance through the lens of Causality](https://mlsanity.com/paper/2201.08413/) (2022)
- [Generalizing Bayesian Optimization with Decision-theoretic Entropies](https://mlsanity.com/paper/2210.01383/) (2022)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Reward-free Alignment for Conflicting Objectives](https://mlsanity.com/paper/2602.02495/) (2026)
- [BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL](https://mlsanity.com/paper/2505.21974/) (2025)
- [Hyperparameter Importance Analysis for Multi-Objective AutoML](https://mlsanity.com/paper/2405.07640/) (2024)

## Abstract (arXiv)

We present PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. The central idea of PESMO is to choose evaluation points so as to maximally reduce the entropy of the posterior distribution over the Pareto set. Critically, the PESMO multi-objective acquisition function can be decomposed as a sum of objective-specific acquisition functions, which enables the algorithm to be used in decoupled scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability also makes it possible to identify difficult objectives that require more evaluations. PESMO also offers gains in efficiency, as its cost scales linearly with the number of objectives, in comparison to the exponential cost of other methods. We compare PESMO with other related methods for multi-objective Bayesian optimization on synthetic and real-world problems. The results show that PESMO produces better recommendations with a smaller number of evaluations of the objectives, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.