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A Small Gain Analysis of Single Timescale Actor Critic

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arxiv 2203.02591 v4 pith:E3WF5ZBV submitted 2022-03-04 math.OC cs.LGcs.SYeess.SY

A Small Gain Analysis of Single Timescale Actor Critic

classification math.OC cs.LGcs.SYeess.SY
keywords criticstationaryactoractor-criticanalysisepsilonfindmethod
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider a version of actor-critic which uses proportional step-sizes and only one critic update with a single sample from the stationary distribution per actor step. We provide an analysis of this method using the small-gain theorem. Specifically, we prove that this method can be used to find a stationary point, and that the resulting sample complexity improves the state of the art for actor-critic methods to $O \left(\mu^{-2} \epsilon^{-2} \right)$ to find an $\epsilon$-approximate stationary point where $\mu$ is the condition number associated with the critic.

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  1. Optimal Sample Complexity for Single Time-Scale Actor-Critic with Momentum

    cs.LG 2026-02 unverdicted novelty 7.0

    Single-timescale actor-critic with STORM momentum and a recent-sample buffer achieves optimal O(ε^{-2}) sample complexity for ε-optimal policies in finite discounted MDPs.