A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization

• URL: http://arxiv.org/abs/2110.08923v3
• Date: Fri, 7 Apr 2023 16:09:21 GMT
• Title: A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization
• Authors: Donghao Ying, Yuhao Ding, Javad Lavaei
• Abstract summary: We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization. Our theoretical analysis shows that its Lagrangian dual function is smooth and the Lagrangian duality gap can be decomposed into the primality gap and the constraint violation.
• Score: 7.483040617090451
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total utility. By leveraging the entropy regularization, our theoretical analysis shows that its Lagrangian dual function is smooth and the Lagrangian duality gap can be decomposed into the primal optimality gap and the constraint violation. Furthermore, we propose an accelerated dual-descent method for entropy-regularized CMDPs. We prove that our method achieves the global convergence rate $\widetilde{\mathcal{O}}(1/T)$ for both the optimality gap and the constraint violation for entropy-regularized CMDPs. A discussion about a linear convergence rate for CMDPs with a single constraint is also provided.

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