Robust Multi-Objective Bayesian Optimization Under Input Noise

TL;DR

This paper introduces a novel multi-objective Bayesian optimization method that is robust to input noise, effectively optimizing multiple uncertain objectives by using a risk measure and scalable algorithms, outperforming existing approaches.

Contribution

It presents the first multi-objective BO approach that explicitly accounts for input noise by optimizing the multivariate value-at-risk, with a scalable, theoretically-grounded optimization technique.

Findings

Significantly outperforms alternative methods in robustness and efficiency.

Effectively identifies designs satisfying multiple specifications with high probability.

Demonstrates practical applicability in manufacturing process optimization.

Abstract

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.