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

• URL: http://arxiv.org/abs/2105.12540v1
• Date: Wed, 26 May 2021 13:35:42 GMT
• Title: Finite-Sample Analysis of Off-Policy Natural Actor-Critic with Linear Function Approximation
• Authors: Zaiwei Chen, Sajad Khodadadian, Siva Theja Maguluri
• Abstract summary: We develop a novel variant of off-policy natural actor-critic algorithm with linear function approximation. We establish a sample complexity of $mathcalO(epsilon-3)$, outperforming all the previously known convergence bounds of such algorithms.
• Score: 5.543220407902113
• License: http://creativecommons.org/licenses/by/4.0/
• 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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