Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913482149986304 |
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| author | Yardim, Batuhan He, Niao |
| author_facet | Yardim, Batuhan He, Niao |
| contents | Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios often feature inherent heterogeneity. Furthermore, most works on MFG assume access to a known MFG model, which might not be readily available for real-world finite-agent games. In this work, we broaden the applicability of MFGs by providing a methodology to extend any finite-player, possibly asymmetric, game to an "induced MFG". First, we prove that $N$-player dynamic games can be symmetrized and smoothly extended to the infinite-player continuum via explicit Kirszbraun extensions. Next, we propose the notion of $α,β$-symmetric games, a new class of dynamic population games that incorporate approximate permutation invariance. For $α,β$-symmetric games, we establish explicit approximation bounds, demonstrating that a Nash policy of the induced MFG is an approximate Nash of the $N$-player dynamic game. We show that TD learning converges up to a small bias using trajectories of the $N$-player game with finite-sample guarantees, permitting symmetrized learning without building an explicit MFG model. Finally, for certain games satisfying monotonicity, we prove a sample complexity of $\widetilde{\mathcal{O}}(\varepsilon^{-6})$ for the $N$-agent game to learn an $\varepsilon$-Nash up to symmetrization bias. Our theory is supported by evaluations on MARL benchmarks with thousands of agents. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_15173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning Yardim, Batuhan He, Niao Computer Science and Game Theory Machine Learning Optimization and Control Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios often feature inherent heterogeneity. Furthermore, most works on MFG assume access to a known MFG model, which might not be readily available for real-world finite-agent games. In this work, we broaden the applicability of MFGs by providing a methodology to extend any finite-player, possibly asymmetric, game to an "induced MFG". First, we prove that $N$-player dynamic games can be symmetrized and smoothly extended to the infinite-player continuum via explicit Kirszbraun extensions. Next, we propose the notion of $α,β$-symmetric games, a new class of dynamic population games that incorporate approximate permutation invariance. For $α,β$-symmetric games, we establish explicit approximation bounds, demonstrating that a Nash policy of the induced MFG is an approximate Nash of the $N$-player dynamic game. We show that TD learning converges up to a small bias using trajectories of the $N$-player game with finite-sample guarantees, permitting symmetrized learning without building an explicit MFG model. Finally, for certain games satisfying monotonicity, we prove a sample complexity of $\widetilde{\mathcal{O}}(\varepsilon^{-6})$ for the $N$-agent game to learn an $\varepsilon$-Nash up to symmetrization bias. Our theory is supported by evaluations on MARL benchmarks with thousands of agents. |
| title | Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning |
| topic | Computer Science and Game Theory Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2408.15173 |