Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation

TL;DR

This paper introduces COMBOO, a new constrained multi-objective Bayesian optimization algorithm that effectively balances active learning and optimization under constraints, with proven theoretical and empirical advantages.

Contribution

The paper presents a novel algorithm COMBOO for constrained multi-objective Bayesian optimization, addressing limitations of previous heuristic methods with theoretical guarantees and practical effectiveness.

Findings

Demonstrates superior sample efficiency on synthetic benchmarks.

Shows effectiveness in real-world applications with constraints.

Provides theoretical analysis supporting the algorithm's performance.

Abstract

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.