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Actor Critic methods have found immense applications on a wide range ofReinforcement Learning tasks especially when the state-action space is large.In this paper, we consider actor critic and natural actor critic algorithmswith function approximation for constrained Markov decision processes (C-MDP)involving inequality constraints and carry out a non-asymptotic analysis forboth of these algorithms in a non-i.i.d (Markovian) setting. We consider thelong-run average cost criterion where both the objective and the constraintfunctions are suitable policy-dependent long-run averages of certain prescribedcost functions. We handle the inequality constraints using the Lagrangemultiplier method. We prove that these algorithms are guaranteed to find afirst-order stationary point (i.e., $\Vert \nabla L(\theta,\gamma)\Vert_2^2\leq \epsilon$) of the performance (Lagrange) function $L(\theta,\gamma)$, witha sample complexity of $\mathcal{\tilde{O}}(\epsilon^{-2.5})$ in the case ofboth Constrained Actor Critic (C-AC) and Constrained Natural Actor Critic(C-NAC) algorithms. We also show the results of experiments on three differentSafety-Gym environments.

Finite-Time Analysis of Three-Timescale Constrained Actor-Critic and Constrained Natural Actor-Critic Algorithms