A Unified Information-Theoretic Approach to Constrained Multi-Fidelity Multi-Objective Bayesian Optimization

2026-10-07

AI Summary

This study addresses the challenges of prohibitive evaluation costs and the absence of unified theoretical guidance for acquisition strategies in multi-objective Bayesian optimization under complex constraints and multi-fidelity settings. To this end, it proposes a unified information-theoretic framework that jointly selects evaluation points and fidelity levels by quantifying the information gain regarding the feasible Pareto front. The core innovation lies in deriving a mixed truncated approximate variational lower bound to construct a cost-aware acquisition function free of heuristic rules, while integrating multi-fidelity surrogate models, mutual information estimation, and Pareto-consistent region modeling to enable efficient inference. Extensive experiments on synthetic, benchmark, and real-world tasks demonstrate that the proposed approach significantly enhances both search efficiency and solution quality for constrained multi-objective optimization.

Abstract

Bayesian optimization often involves multiple objectives, constraints, and fidelity levels. We address the challenge of jointly selecting where and at which fidelity to evaluate to identify the highest-fidelity feasible Pareto frontier in this combined setting. From a unified information-theoretic perspective, we measure query utility by the information gain about this frontier, provided by an observation. Since this mutual information is intractable, we derive a variational lower bound using a mixture of under- and over-truncated approximations to the Pareto-consistent region. Multi-fidelity surrogate models propagate the information to arbitrary fidelities, yielding a cost-aware acquisition function without separate heuristics for fidelity selection or constraint handling. Experiments on synthetic, benchmark, and real-world problems demonstrate effectiveness across diverse objective, constraint, and fidelity settings.

Problem

• Bayesian optimization
• multi-objective
• multi-fidelity
• constrained optimization
• Pareto frontier

Innovation

• Multi-Fidelity Bayesian Optimization
• Information-Theoretic Acquisition
• Multi-Objective Optimization
• Variational Lower Bound
• Constrained Optimization