Learning Mean-Field Games through Mean-Field Actor-Critic Flow
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914110990450688 |
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| author | Zhou, Mo Zhou, Haosheng Hu, Ruimeng |
| author_facet | Zhou, Mo Zhou, Haosheng Hu, Ruimeng |
| contents | We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and optimal transport. The MFAC framework jointly evolves the control (actor), value function (critic), and distribution components through coupled gradient-based updates governed by partial differential equations (PDEs). A central innovation is the Optimal Transport Geodesic Picard (OTGP) flow, which drives the distribution toward equilibrium along Wasserstein-2 geodesics. We conduct a rigorous convergence analysis using Lyapunov functionals and establish global exponential convergence of the MFAC flow under a suitable timescale. Our results highlight the algorithmic interplay among actor, critic, and distribution components. Numerical experiments illustrate the theoretical findings and demonstrate the effectiveness of the MFAC framework in computing MFG equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Mean-Field Games through Mean-Field Actor-Critic Flow Zhou, Mo Zhou, Haosheng Hu, Ruimeng Optimization and Control Machine Learning 35Q89, 49N80 We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and optimal transport. The MFAC framework jointly evolves the control (actor), value function (critic), and distribution components through coupled gradient-based updates governed by partial differential equations (PDEs). A central innovation is the Optimal Transport Geodesic Picard (OTGP) flow, which drives the distribution toward equilibrium along Wasserstein-2 geodesics. We conduct a rigorous convergence analysis using Lyapunov functionals and establish global exponential convergence of the MFAC flow under a suitable timescale. Our results highlight the algorithmic interplay among actor, critic, and distribution components. Numerical experiments illustrate the theoretical findings and demonstrate the effectiveness of the MFAC framework in computing MFG equilibria. |
| title | Learning Mean-Field Games through Mean-Field Actor-Critic Flow |
| topic | Optimization and Control Machine Learning 35Q89, 49N80 |
| url | https://arxiv.org/abs/2510.12180 |