Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach

TL;DR

This paper introduces a multi-fidelity Bayesian optimization method that efficiently approximates the Pareto front in multi-objective problems by maximizing information gain per resource, outperforming existing single-fidelity algorithms.

Contribution

It proposes MF-OSEMO, a novel multi-fidelity entropy search approach for multi-objective optimization that effectively balances resource use and solution accuracy.

Findings

MF-OSEMO significantly outperforms single-fidelity algorithms.

The method effectively balances resource consumption and optimization accuracy.

Experimental results on synthetic and real-world problems validate its effectiveness.

Abstract

We study the novel problem of blackbox optimization of multiple objectives via multi-fidelity function evaluations that vary in the amount of resources consumed and their accuracy. The overall goal is to approximate the true Pareto set of solutions by minimizing the resources consumed for function evaluations. For example, in power system design optimization, we need to find designs that trade-off cost, size, efficiency, and thermal tolerance using multi-fidelity simulators for design evaluations. In this paper, we propose a novel approach referred as Multi-Fidelity Output Space Entropy Search for Multi-objective Optimization (MF-OSEMO) to solve this problem. The key idea is to select the sequence of candidate input and fidelity-vector pairs that maximize the information gained about the true Pareto front per unit resource cost. Our experiments on several synthetic and real-world benchmark problems show that MF-OSEMO, with both approximations, significantly improves over the state-of-the-art single-fidelity algorithms for multi-objective optimization.