Finite-Sample Analysis of Off-Policy Natural Actor-Critic with Linear Function Approximation
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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 𝒪(ϵ^-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 𝒪(1/T) after T iterations. Combining the finite sample error bounds of actor and the critic, we obtain the 𝒪(ϵ^-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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