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    Training strategies for competing multiagent dynamical systems

    Haotian Dai1, Marco G. Mazza2, Yunyun Li3,*, Fabio Marchesoni3,4, and Sergey Savel'ev1

    • 1Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
    • 2Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
    • 3MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
    • 4Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy

    • *Contact author: yunyunli@tongji.edu.cn

    Phys. Rev. E 112, 065310 – Published 15 December, 2025

    DOI: https://doi.org/10.1103/36rk-41pp

    Abstract

    We explore competitive dynamics in multiagent active matter systems using reinforcement learning. In our study, two active Brownian particles (referred to as predators) were trained using either simultaneous or sequential protocols to capture ten passive Brownian particles (preys). The training results depend on the agent, and generally one agent tends to overperform the other. To assess the effectiveness of the two protocols, we examined two policies: (i) a natural policy, where updates to the reinforcement learning parameters of both predators were stopped at a fixed time, even if one agent performed suboptimally; and (ii) a hybrid policy, where we combined the reinforcement learning parameters recorded when each agent achieved its optimal performance. If limited to natural training, simultaneous training appears to be the better option. However, when hybrid training is also allowed, sequential training becomes the preferred choice.

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