# Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints

arXiv: https://arxiv.org/abs/1609.01051 · HTML: https://mlsanity.com/paper/1609.01051/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2016.

## Built on by (most cited first, 27 of 27)

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- [Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method](https://mlsanity.com/paper/2207.03842/) (2022)
- [Constrained multi-objective optimization of process design parameters in settings with scarce data: an application to adhesive bonding](https://mlsanity.com/paper/2112.08760/) (2021)
- [Non-Myopic Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2412.08085/) (2024)
- [High-dimensional Multi-objective Bayesian Optimization with Learned Variable Interactions](https://mlsanity.com/paper/2608.11713/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)
- [Portfolio-Based Constrained Multi-Objective Bayesian Optimization for Materials Design](https://mlsanity.com/paper/2609.19550/) (2026)
- [Learning What to Evaluate: Correlation-Aware Decoupling for Multiobjective Bayesian Optimization](https://mlsanity.com/paper/2609.32632/) (2026)

## Abstract (arXiv)

This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. PESMOC can hence be used to solve a wide range of optimization problems. Iteratively, PESMOC chooses an input location on which to evaluate the objective functions and the constraints so as to maximally reduce the entropy of the Pareto set of the corresponding optimization problem. The constraints considered in PESMOC are assumed to have similar properties to those of the objective functions in typical Bayesian optimization problems. That is, they do not have a known expression (which prevents gradient computation), their evaluation is considered to be very expensive, and the resulting observations may be corrupted by noise. These constraints arise in a plethora of expensive black-box optimization problems. We carry out synthetic experiments to illustrate the effectiveness of PESMOC, where we sample both the objectives and the constraints from a Gaussian process prior. The results obtained show that PESMOC is able to provide better recommendations with a smaller number of evaluations than a strategy based on random search.