Hypervolume-based Multi-objective Bayesian Optimization with Student-t Processes

TL;DR

This paper introduces a novel multi-objective Bayesian optimization method using Student-$t$ processes, providing an analytical hypervolume-based improvement criterion that outperforms traditional Gaussian process approaches on complex problems.

Contribution

It develops an analytical hypervolume-based probability of improvement for Student-$t$ processes in multi-objective optimization, enhancing flexibility and performance.

Findings

Effective on difficult multi-objective problems

Outperforms Gaussian process-based methods

Provides analytical expression for hypervolume improvement

Abstract

Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the hypervolume-based probability of improvement is developed for independent Student-$t$ process priors of the objectives. Its effectiveness is shown on a multi-objective optimization problem which is known to be difficult with traditional Gaussian processes.