Model Predictive Control

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Model Predictive Control

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Lyapunov Function

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Adaptive Controller

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Optimal Control

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Stochastic Optimal Control

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Model Predictive Path Integral

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Closed-Loop Control

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Linear Quadratic Regulator

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Discrete-Time Linear Systems

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653 papers

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May 13, 2026 · cs.LGJ/K move · Enter open · S save

Achieving $ε^{-2}$ Sample Complexity for Single-Loop Actor-Critic under Minimal Assumptions

Ishaq Hamza, Zaiwei Chen

IISc · Edwardson School of Industrial Engineering, Purdue University · Purdue IE

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first

\tilde{\mathcal{O}}(ε^{-2})

sample complexity guarantee for finding an

ε

-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an

\tilde{\mathcal{O}}(ε^{-2})

sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an

\tilde{\mathcal{O}}(1/T)

convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

Soft Actor-Critic Optimal Policies Optimal Sample Complexity Lyapunov Function Minimal

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