  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.
