Mean-Field Bayesian Optimisation

TL;DR

This paper introduces MF-GP-UCB, a scalable Bayesian Optimization algorithm leveraging mean-field assumptions, with theoretical guarantees and superior empirical performance on real-world large-agent problems.

Contribution

It presents a novel mean-field Bayesian Optimization method with a regret bound independent of the number of agents, improving scalability and efficiency.

Findings

MF-GP-UCB outperforms existing benchmarks in diverse tasks.

Theoretical regret bound is independent of agent count.

Empirical results show substantial performance improvements.

Abstract

We address the problem of optimising the average payoff for a large number of cooperating agents, where the payoff function is unknown and treated as a black box. While standard Bayesian Optimisation (BO) methods struggle with the scalability required for high-dimensional input spaces, we demonstrate how leveraging the mean-field assumption on the black-box function can transform BO into an efficient and scalable solution. Specifically, we introduce MF-GP-UCB, a novel efficient algorithm designed to optimise agent payoffs in this setting. Our theoretical analysis establishes a regret bound for MF-GP-UCB that is independent of the number of agents, contrasting sharply with the exponential dependence observed when naive BO methods are applied. We evaluate our algorithm on a diverse set of tasks, including real-world problems, such as optimising the location of public bikes for a bike-sharing programme, distributing taxi fleets, and selecting refuelling ports for maritime vessels. Empirical results demonstrate that MF-GP-UCB significantly outperforms existing benchmarks, offering substantial improvements in performance and scalability, constituting a promising solution for mean-field, black-box optimisation. The code is available at https://github.com/petarsteinberg/MF-BO.