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

• URL: http://arxiv.org/abs/2310.16363v3
• Date: Wed, 29 May 2024 05:54:19 GMT
• Title: Finite-Time Analysis of Three-Timescale Constrained Actor-Critic and Constrained Natural Actor-Critic Algorithms
• Authors: Prashansa Panda, Shalabh Bhatnagar,
• Abstract summary: We consider actor critic and natural actor critic algorithms with function approximation for constrained Markov decision processes. We carry out a non-asymptotic analysis for both of these algorithms in a non-i.i.d (Markovian) setting. We also show the results of experiments on three different Safety-Gym environments.
• Score: 5.945710235932345
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Actor Critic methods have found immense applications on a wide range of Reinforcement Learning tasks especially when the state-action space is large. In this paper, we consider actor critic and natural actor critic algorithms with function approximation for constrained Markov decision processes (C-MDP) involving inequality constraints and carry out a non-asymptotic analysis for both of these algorithms in a non-i.i.d (Markovian) setting. We consider the long-run average cost criterion where both the objective and the constraint functions are suitable policy-dependent long-run averages of certain prescribed cost functions. We handle the inequality constraints using the Lagrange multiplier method. We prove that these algorithms are guaranteed to find a first-order stationary point (i.e., $\Vert \nabla L(\theta,\gamma)\Vert_2^2 \leq \epsilon$) of the performance (Lagrange) function $L(\theta,\gamma)$, with a sample complexity of $\mathcal{\tilde{O}}(\epsilon^{-2.5})$ in the case of both Constrained Actor Critic (C-AC) and Constrained Natural Actor Critic (C-NAC) algorithms. We also show the results of experiments on three different Safety-Gym environments.

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