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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07082 |
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| _version_ | 1866914831548809216 |
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| author | Dai, Yan Cui, Qiwen Du, Simon S. |
| author_facet | Dai, Yan Cui, Qiwen Du, Simon S. |
| contents | Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable until several recent works (Daskalakis et al., 2023; Cui et al., 2023; Wang et al., 2023). While these works resolved the curse of multi-agents, when the state spaces are prohibitively large and (linear) function approximations are deployed, they either had a slower convergence rate of $O(T^{-1/4})$ or brought a polynomial dependency on the number of actions $A_{\max}$ -- which is avoidable in single-agent cases even when the loss functions can arbitrarily vary with time. This paper first refines the AVLPR framework by Wang et al. (2023), with an insight of designing *data-dependent* (i.e., stochastic) pessimistic estimation of the sub-optimality gap, allowing a broader choice of plug-in algorithms. When specialized to MGs with independent linear function approximations, we propose novel *action-dependent bonuses* to cover occasionally extreme estimation errors. With the help of state-of-the-art techniques from the single-agent RL literature, we give the first algorithm that tackles the curse of multi-agents, attains the optimal $O(T^{-1/2})$ convergence rate, and avoids $\text{poly}(A_{\max})$ dependency simultaneously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined Sample Complexity for Markov Games with Independent Linear Function Approximation Dai, Yan Cui, Qiwen Du, Simon S. Machine Learning Computer Science and Game Theory Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable until several recent works (Daskalakis et al., 2023; Cui et al., 2023; Wang et al., 2023). While these works resolved the curse of multi-agents, when the state spaces are prohibitively large and (linear) function approximations are deployed, they either had a slower convergence rate of $O(T^{-1/4})$ or brought a polynomial dependency on the number of actions $A_{\max}$ -- which is avoidable in single-agent cases even when the loss functions can arbitrarily vary with time. This paper first refines the AVLPR framework by Wang et al. (2023), with an insight of designing *data-dependent* (i.e., stochastic) pessimistic estimation of the sub-optimality gap, allowing a broader choice of plug-in algorithms. When specialized to MGs with independent linear function approximations, we propose novel *action-dependent bonuses* to cover occasionally extreme estimation errors. With the help of state-of-the-art techniques from the single-agent RL literature, we give the first algorithm that tackles the curse of multi-agents, attains the optimal $O(T^{-1/2})$ convergence rate, and avoids $\text{poly}(A_{\max})$ dependency simultaneously. |
| title | Refined Sample Complexity for Markov Games with Independent Linear Function Approximation |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2402.07082 |