Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator
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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_ | 1866912365834928128 |
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| author | Chen, Xuyang Duan, Jingliang Zhao, Lin |
| author_facet | Chen, Xuyang Duan, Jingliang Zhao, Lin |
| contents | Actor-critic methods have achieved state-of-the-art performance in various challenging tasks. However, theoretical understandings of their performance remain elusive and challenging. Existing studies mostly focus on practically uncommon variants such as double-loop or two-timescale stepsize actor-critic algorithms for simplicity. These results certify local convergence on finite state- or action-space only. We push the boundary to investigate the classic single-sample single-timescale actor-critic on continuous (infinite) state-action space, where we employ the canonical linear quadratic regulator (LQR) problem as a case study. We show that the popular single-timescale actor-critic can attain an epsilon-optimal solution with an order of epsilon to -2 sample complexity for solving LQR on the demanding continuous state-action space. Our work provides new insights into the performance of single-timescale actor-critic, which further bridges the gap between theory and practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator Chen, Xuyang Duan, Jingliang Zhao, Lin Machine Learning Actor-critic methods have achieved state-of-the-art performance in various challenging tasks. However, theoretical understandings of their performance remain elusive and challenging. Existing studies mostly focus on practically uncommon variants such as double-loop or two-timescale stepsize actor-critic algorithms for simplicity. These results certify local convergence on finite state- or action-space only. We push the boundary to investigate the classic single-sample single-timescale actor-critic on continuous (infinite) state-action space, where we employ the canonical linear quadratic regulator (LQR) problem as a case study. We show that the popular single-timescale actor-critic can attain an epsilon-optimal solution with an order of epsilon to -2 sample complexity for solving LQR on the demanding continuous state-action space. Our work provides new insights into the performance of single-timescale actor-critic, which further bridges the gap between theory and practice. |
| title | Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.01041 |