A Robust Multi-Objective Bayesian Optimization Framework Considering Input Uncertainty

TL;DR

This paper introduces a new Bayesian optimization framework that efficiently finds robust multi-objective solutions considering input uncertainty, using a robust Gaussian Process model and a two-stage search process, demonstrated on numerical benchmarks.

Contribution

It presents a novel multi-objective Bayesian optimization framework that accounts for input uncertainty and employs a robust Gaussian Process model with a two-stage search process.

Findings

Effective in identifying robust Pareto frontiers

Supports various input uncertainty distributions

Leverages parallel computing for efficiency

Abstract

Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to efficiently perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer the Bayes risk criterion to quantify robustness, and we develop a two-stage Bayesian optimization process to search for a robust Pareto frontier. The complete framework supports various distributions of the input uncertainty and takes full advantage of parallel computing. We demonstrate the effectiveness of the framework through numerical benchmarks.