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arXiv · 2505.01041

Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator

Xuyang Chen·Jingliang Duan·Lin Zhao
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Abstract

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.

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Xuyang Chen, Jingliang Duan, Lin Zhao. 2025-05-02. Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator. https://doi.org/10.24963/ijcai.2024%2F422

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