Stochastic Policy Gradient Methods: Improved Sample Complexity for Fisher-non-degenerate Policies
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Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a 𝒪̃(ε^-2.5) sample complexity of this method for finding a global ε-optimal policy. Improving over the previously known 𝒪̃(ε^-3) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to 𝒪̃(ε^-2) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.
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