Policy-based Primal-Dual Methods for Concave CMDP with Variance Reduction

Code

• github.com/hyunin-lee/vr-pdpg
  OfficialIn paperpytorch★ 3

Abstract

We study Concave Constrained Markov Decision Processes (Concave CMDPs) where both the objective and constraints are defined as concave functions of the state-action occupancy measure. We propose the Variance-Reduced Primal-Dual Policy Gradient Algorithm (VR-PDPG), which updates the primal variable via policy gradient ascent and the dual variable via projected sub-gradient descent. Despite the challenges posed by the loss of additivity structure and the nonconcave nature of the problem, we establish the global convergence of VR-PDPG by exploiting a form of hidden concavity. In the exact setting, we prove an O(T^-1/3) convergence rate for both the average optimality gap and constraint violation, which further improves to O(T^-1/2) under strong concavity of the objective in the occupancy measure. In the sample-based setting, we demonstrate that VR-PDPG achieves an O(^-4) sample complexity for -global optimality. Moreover, by incorporating a diminishing pessimistic term into the constraint, we show that VR-PDPG can attain a zero constraint violation without compromising the convergence rate of the optimality gap. Finally, we validate the effectiveness of our methods through numerical experiments.

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