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

Machine Learning (cs.LG)

arXiv:2610.10174 [cs.LG]

(or arXiv:2610.10174v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.10174 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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