Mean-Field Bayesian Optimisation

2025-02-17

AI Summary

We address the problem of optimizing the average reward in large-scale cooperative multi-agent systems, where the reward function is an unknown black-box and its input dimensionality grows prohibitively with the number of agents—rendering standard Bayesian optimization (BO) intractable. To this end, we propose MF-GP-UCB, the first BO framework incorporating the mean-field assumption. It jointly leverages Gaussian process modeling, an upper-confidence-bound (UCB) acquisition strategy, and mean-field approximation to achieve a theoretical regret bound independent of the agent count. The algorithm is provably scalable and supports fully distributed implementation. Empirical evaluation on real-world applications—including bike-sharing station placement, taxi fleet dispatch, and maritime refueling port selection—demonstrates that MF-GP-UCB significantly outperforms state-of-the-art BO and multi-agent optimization baselines, achieving both high empirical performance and strong scalability.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Optimise average payoff for cooperating agents
• Overcome scalability in high-dimensional input spaces
• Introduce MF-GP-UCB for efficient black-box optimisation

Innovation

• Mean-Field Bayesian Optimisation
• MF-GP-UCB algorithm
• Scalable black-box optimisation