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.