Block Policy Mirror Descent
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In this paper, we present a new class of policy gradient (PG) methods, namely the block policy mirror descent (BPMD) methods for solving a class of regularized reinforcement learning (RL) problems with (strongly) convex regularizers. Compared to the traditional PG methods with batch update rule, which visit and update the policy for every state, BPMD methods have cheap per-iteration computation via a partial update rule that performs the policy update on a sampled state. Despite the nonconvex nature of the problem and a partial update rule, BPMD methods achieve fast linear convergence to the global optimality. We further extend BPMD methods to the stochastic setting, by utilizing stochastic first-order information constructed from samples. We establish (1/ϵ) (resp. (1/ϵ^2)) sample complexity for the strongly convex (resp. non-strongly convex) regularizers, with different procedures for constructing the stochastic first-order information, where ϵ denotes the target accuracy. To the best of our knowledge, this is the first time that block coordinate descent methods have been developed and analyzed for policy optimization in reinforcement learning.
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