A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations

TL;DR

This paper introduces a flexible, cost-effective Bayesian optimization framework using random scalarizations to target specific regions of the Pareto front, achieving low regret in multi-objective problems.

Contribution

It proposes a novel random scalarization approach for multi-objective Bayesian optimization that allows targeting specific Pareto regions and demonstrates sublinear regret.

Findings

Outperforms traditional methods in flexibility and efficiency

Achieves sublinear regret in multi-objective optimization

Effective on synthetic and real-world problems

Abstract

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.