# Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints

arXiv: https://arxiv.org/abs/2009.01721 · HTML: https://mlsanity.com/paper/2009.01721/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2020.

## Built on by (most cited first, 30 of 81)

- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
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- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [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)
- [OpenBox: A Generalized Black-box Optimization Service](https://mlsanity.com/paper/2106.00421/) (2021)
- [Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spaces](https://mlsanity.com/paper/2111.01186/) (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)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Multi-objective Asynchronous Successive Halving](https://mlsanity.com/paper/2106.12639/) (2021)
- [Efficiently Controlling Multiple Risks with Pareto Testing](https://mlsanity.com/paper/2210.07913/) (2022)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Bayesian Optimization over Permutation Spaces](https://mlsanity.com/paper/2112.01049/) (2021)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.06980/) (2021)
- [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)
- [Multi-Objective Optimization of ReRAM Crossbars for Robust DNN Inferencing under Stochastic Noise](https://mlsanity.com/paper/2109.05437/) (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)
- [OpenBox: A Python Toolkit for Generalized Black-box Optimization](https://mlsanity.com/paper/2304.13339/) (2023)

## Abstract (arXiv)

We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number of function evaluations. For example, in aviation power system design applications, we need to find the designs that trade-off total energy and the mass while satisfying specific thresholds for motor temperature and voltage of cells. This optimization requires performing expensive computational simulations to evaluate designs. In this paper, we propose a new approach referred as em Max-value Entropy Search for Multi-objective Optimization with Constraints (MESMOC) to solve this problem. MESMOC employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation to uncover high-quality pareto-set solutions while satisfying constraints. We apply MESMOC to two real-world engineering design applications to demonstrate its effectiveness over state-of-the-art algorithms.