Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

TL;DR

This paper introduces PALS, an extension of Pareto Active Learning, tailored for multi-objective optimization of stochastic simulators with high variance, demonstrating superior performance over existing methods.

Contribution

The paper presents PALS, a novel Bayesian optimization algorithm specifically designed for stochastic simulators, extending the PAL method to handle stochasticity effectively.

Findings

PALS outperforms scalarization-based approaches.

PALS achieves better Pareto front estimation.

Numerical experiments validate PALS's efficiency.

Abstract

This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. The proposed approach is an extension of the Pareto Active Learning (PAL) algorithm for the estimation of Pareto-optimal solutions that makes it suitable for the stochastic setting. We named it Pareto Active Learning for Stochastic Simulators (PALS). The performance of PALS is assessed through numerical experiments over a set of bi-dimensional, bi-objective test problems. PALS exhibits superior performance when compared to other scalarization-based and random-search approaches.