Algorithm for Constrained Markov Decision Process with Linear Convergence
This work addresses the problem of optimizing policies under constraints in reinforcement learning for agents, representing an incremental improvement over prior primal-dual approaches.
The paper tackles the constrained Markov decision process problem by proposing a new dual approach that integrates entropy regularized policy optimization and Vaidya's dual optimizer, achieving linear convergence to the global optimum with improved complexity in terms of optimality gap and constraint violation compared to existing methods.
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy regularized policy optimizer and Vaidya's dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.