Multi-Objective Bayesian Optimization with Active Preference Learning

TL;DR

This paper introduces a Bayesian optimization method that efficiently finds the most preferred solution in multi-objective problems by actively learning the decision maker's preferences, reducing interaction costs and focusing on practical solutions.

Contribution

It presents a novel active preference learning approach within Bayesian optimization to identify preferred solutions in multi-objective problems with minimal DM interaction.

Findings

Effective in benchmark function optimization

Successful hyper-parameter optimization for ML models

Reduces interaction cost with decision maker

Abstract

There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective functions and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.