# Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation

arXiv: https://arxiv.org/abs/2411.03641 · HTML: https://mlsanity.com/paper/2411.03641/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 66 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 30 of 36)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Gaussian Process Bandit Optimization with Few Batches](https://mlsanity.com/paper/2110.07788/) (2021)
- [Predictive Entropy Search for Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1502.05312/) (2015)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (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)
- [Computer-Aided Multi-Objective Optimization in Small Molecule Discovery](https://mlsanity.com/paper/2210.07209/) (2022)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [Constrained Bayesian Optimization with Max-Value Entropy Search](https://mlsanity.com/paper/1910.07003/) (2019)
- [Improved Max-value Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2011.01150/) (2020)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)

## Built on by (most cited first, 6 of 6)

- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Multi-Objective Coverage via Constraint Active Search](https://mlsanity.com/paper/2602.15595/) (2026)
- [Multi-Objective Bayesian Optimization via Adaptive varepsilon-Constraints Decomposition](https://mlsanity.com/paper/2604.15959/) (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)

## Abstract (arXiv)

Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on certain attributes of the experimental outcomes. Previous work has primarily focused on constrained single-objective optimization tasks or active search under constraints. The existing constrained multi-objective algorithms address the issue with heuristics and approximations, posing challenges to the analysis of the sample efficiency. We propose a novel constrained multi-objective Bayesian optimization algorithm COMBOO that balances active learning of the level-set defined on multiple unknowns with multi-objective optimization within the feasible region. We provide both theoretical analysis and empirical evidence, demonstrating the efficacy of our approach on various synthetic benchmarks and real-world applications.