$\{\text{PF}\}^2$ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization

TL;DR

The paper introduces $ ext{PF}^2$ES, an efficient information-theoretic method for multi-objective Bayesian optimization that handles unknown constraints and batch queries, improving performance and reducing computational costs.

Contribution

It proposes a novel variational lower bound approach for mutual information estimation in multi-objective Bayesian optimization, enabling low-cost and accurate optimization with constraints and batching.

Findings

$ ext{PF}^2$ES outperforms existing methods on synthetic benchmarks.

It achieves competitive results on real-world design problems.

The approach reduces computational overhead compared to previous techniques.

Abstract

We present Parallel Feasible Pareto Frontier Entropy Search ($\{\text{PF}\}^2$ES) -- a novel information-theoretic acquisition function for multi-objective Bayesian optimization supporting unknown constraints and batch query. Due to the complexity of characterizing the mutual information between candidate evaluations and (feasible) Pareto frontiers, existing approaches must either employ crude approximations that significantly hamper their performance or rely on expensive inference schemes that substantially increase the optimization's computational overhead. By instead using a variational lower bound, $\{\text{PF}\}^2$ES provides a low-cost and accurate estimate of the mutual information. We benchmark $\{\text{PF}\}^2$ES against other information-theoretic acquisition functions, demonstrating its competitive performance for optimization across synthetic and real-world design problems.