A General Markov Decision Process Framework for Directly Learning Optimal Control Policies
This work addresses the challenge of directly learning optimal policies in RL, offering a novel framework that could impact control applications, though it appears incremental in extending classical methods.
The paper tackles the problem of learning optimal control policies in reinforcement learning by introducing a new MDP framework that generalizes the Bellman operator and policy definitions, and demonstrates significant empirical benefits with quantified results.
We consider a new form of reinforcement learning (RL) that is based on opportunities to directly learn the optimal control policy and a general Markov decision process (MDP) framework devised to support these opportunities. Derivations of general classes of our control-based RL methods are presented, together with forms of exploration and exploitation in learning and applying the optimal control policy over time. Our general MDP framework extends the classical Bellman operator and optimality criteria by generalizing the definition and scope of a policy for any given state. We establish the convergence and optimality-both in general and within various control paradigms (e.g., piecewise linear control policies)-of our control-based methods through this general MDP framework, including convergence of $Q$-learning within the context of our MDP framework. Our empirical results demonstrate and quantify the significant benefits of our approach.