## Finite-time Analysis of Single-timescale Actor-Critic on Linear Quadratic Regulator

22 Sept 2022, 12:34 (modified: 09 Nov 2022, 11:30)ICLR 2023 Conference Blind SubmissionReaders: Everyone
Keywords: single-timescale actor-critic, linear quadratic regulator
TL;DR: Finite-time convergence of single-sample single-timescale actor-critic with a global optimality guarantee
Abstract: Actor-critic (AC) methods have achieved state-of-the-art performance in many challenging tasks. However, their convergence in most practical applications are still poorly understood. Existing works mostly consider the uncommon double-loop or two-timescale stepsize variants for the ease of analysis. We investigate the practical yet more challenging vanilla single-sample single-timescale AC for solving the canonical linear quadratic regulator problem. Specifically, the actor and the critic update only once with a single sample in each iteration using proportional stepsizes. We prove that the vanilla AC can attain an $\epsilon$-optimal solution with a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-2})$, which elucidates on the practical efficiency of single-sample single-timescale AC. We develop a novel analysis framework that directly bounds the whole interconnected iteration system without the conservative decoupling commonly adopted in previous analysis of AC. Our work presents the first finite-time analysis of single-sample single-timescale AC with a global optimality guarantee.
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