A Novel Framework for Policy Mirror Descent with General Parametrization and Linear Convergence

Modern policy optimization methods in applied reinforcement learning, such as Trust Region Policy Optimization and Policy Mirror Descent, are often based on the policy gradient framework. While theoretical guarantees have been established for this class of algorithms, particularly in the tabular setting, the use of a general parametrization scheme remains mostly unjustified. In this work, we introduce a novel framework for policy optimization based on mirror descent that naturally accommodates general parametrizations. The policy class induced by our scheme recovers known classes, e.g. softmax, and it generates new ones, depending on the choice of the mirror map. For a general mirror map and parametrization class, we establish the quasi-monotonicity of the updates in value function, global linear convergence rates, and we bound the total expected Bregman divergence of the algorithm along its path. To showcase the ability of our framework to accommodate general parametrization schemes, we present a case study involving shallow neural networks.