A Robust Multi-Objective Bayesian Optimization Framework Considering Input Uncertainty
This work addresses the need for robust solutions in engineering design and similar applications where multiple objectives and input uncertainties must be considered, representing an incremental advancement in extending Bayesian optimization methods.
The paper tackles the problem of multi-objective Bayesian optimization under input uncertainty, which is less explored compared to single-objective cases, by introducing a novel framework that uses a robust Gaussian Process model and a two-stage process to efficiently find a robust Pareto frontier, demonstrating effectiveness through numerical benchmarks.
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.