Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies

• URL: http://arxiv.org/abs/2210.01400v1
• Date: Tue, 4 Oct 2022 06:17:52 GMT
• Title: Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies
• Authors: Rui Yuan, Simon S. Du, Robert M. Gower, Alessandro Lazaric, Lin Xiao
• Abstract summary: We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. We show that both methods attain linear convergence rates and $mathcalO (1/epsilon2)$ sample complexities using a simple, non-adaptive geometrically increasing step size.
• Score: 115.86431674214282
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. Using the compatible function approximation framework, both methods with log-linear policies can be written as approximate versions of the policy mirror descent (PMD) method. We show that both methods attain linear convergence rates and $\mathcal{O}(1/\epsilon^2)$ sample complexities using a simple, non-adaptive geometrically increasing step size, without resorting to entropy or other strongly convex regularization. Lastly, as a byproduct, we obtain sublinear convergence rates for both methods with arbitrary constant step size.

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