Algorithm for Constrained Markov Decision Process with Linear Convergence

TL;DR

This paper introduces a novel dual approach combining entropy regularization and Vaidya's optimizer for constrained Markov decision processes, achieving linear convergence and improved complexity bounds.

Contribution

It proposes a new dual method integrating entropy regularization and Vaidya's optimizer, enabling faster convergence in constrained MDPs with nonconcave objectives.

Findings

Achieves linear convergence rate to the global optimum.

Provides finite-time error bounds for the proposed method.

Significantly improves complexity over existing primal-dual approaches.

Abstract

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.