Choice functions based multi-objective Bayesian optimisation

TL;DR

This paper introduces a Bayesian framework for multi-objective optimization that learns from choice-based feedback rather than explicit function evaluations, enabling optimization in scenarios with limited or preference-based data.

Contribution

It develops a novel Gaussian process-based model for choice data and applies it to multi-objective Bayesian optimization, addressing a new class of problems.

Findings

Effective modeling of choice-based preferences

Successful application to multi-objective optimization

New likelihood model for choice data

Abstract

In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension $n_e$ which embeds the options into the real vector space of dimension n, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.