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arXiv · 2105.12540

Finite-Sample Analysis of Off-Policy Natural Actor-Critic with Linear Function Approximation

Zaiwei Chen·Sajad Khodadadian·Siva Theja Maguluri
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Abstract

In this paper, we develop a novel variant of off-policy natural actor-critic algorithm with linear function approximation and we establish a sample complexity of $\mathcal{O}(\epsilon^{-3})$, outperforming all the previously known convergence bounds of such algorithms. In order to overcome the divergence due to deadly triad in off-policy policy evaluation under function approximation, we develop a critic that employs $n$-step TD-learning algorithm with a properly chosen $n$. We present finite-sample convergence bounds on this critic under both constant and diminishing step sizes, which are of independent interest. Furthermore, we develop a variant of natural policy gradient under function approximation, with an improved convergence rate of $\mathcal{O}(1/T)$ after $T$ iterations. Combining the finite sample error bounds of actor and the critic, we obtain the $\mathcal{O}(\epsilon^{-3})$ sample complexity. We derive our sample complexity bounds solely based on the assumption that the behavior policy sufficiently explores all the states and actions, which is a much lighter assumption compared to the related literature.

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Zaiwei Chen, Sajad Khodadadian, Siva Theja Maguluri. 2021-05-26. Finite-Sample Analysis of Off-Policy Natural Actor-Critic with Linear Function Approximation. https://arxiv.org/abs/2105.12540

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