Mean-Field Bayesian Optimisation

• URL: http://arxiv.org/abs/2502.12315v1
• Date: Mon, 17 Feb 2025 20:34:29 GMT
• Title: Mean-Field Bayesian Optimisation
• Authors: Petar Steinberg, Juliusz Ziomek, Matej Jusup, Ilija Bogunovic,
• Abstract summary: 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. We introduce MF-GP-UCB, a novel efficient algorithm designed to optimise agent payoffs in this setting. Empirical results demonstrate that MF-GP-UCB significantly outperforms existing benchmarks.
• Score: 11.624033826631448
• License:
• 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.

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