Mean-Field Bayesian Optimisation
This provides a scalable solution for mean-field black-box optimization problems affecting multi-agent systems in domains like transportation and logistics.
The paper tackles the problem of optimizing average payoff for many cooperating agents with unknown black-box payoff functions, where standard Bayesian Optimization methods struggle with scalability. The proposed MF-GP-UCB algorithm achieves a regret bound independent of the number of agents and significantly outperforms existing benchmarks in tasks like bike-sharing optimization and taxi fleet distribution.
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.