A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization
This work addresses constrained reinforcement learning problems for agents needing to balance optimization with constraints, representing an incremental improvement in algorithmic convergence.
The paper tackles constrained Markov decision processes (CMDPs) with entropy regularization by proposing an accelerated dual-descent method, achieving a global convergence rate of O~(1/T) for both optimality gap and constraint violation.
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.