# A Finite Time Analysis of Two Time-Scale Actor Critic Methods

arXiv: https://arxiv.org/abs/2005.01350 · HTML: https://mlsanity.com/paper/2005.01350/

## Key facts

- Cited by 122 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 30 of 122)

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- [A Small Gain Analysis of Single Timescale Actor Critic](https://mlsanity.com/paper/2203.02591/) (2022)
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- [Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Path](https://mlsanity.com/paper/2208.11639/) (2022)
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- [Global Optimality and Finite Sample Analysis of Softmax Off-Policy Actor Critic under State Distribution Mismatch](https://mlsanity.com/paper/2111.02997/) (2021)

## Abstract (arXiv)

Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i.i.d. setting. We prove that the actor-critic method is guaranteed to find a first-order stationary point (i.e., |nabla J(boldsymbolθ)|22 ≤ ε) of the non-concave performance function J(boldsymbolθ), with mathcaltildeO(ε-2.5) sample complexity. To the best of our knowledge, this is the first work providing finite-time analysis and sample complexity bound for two time-scale actor-critic methods.