# A General Markov Decision Process Framework for Directly Learning Optimal Control Policies

## TL;DR

This paper introduces a new reinforcement learning framework based on a generalized Markov decision process that directly learns optimal control policies, extending classical methods and demonstrating improved empirical performance.

## Contribution

It proposes a novel MDP framework that generalizes policy definitions and supports direct learning of optimal control policies, including convergence proofs and empirical validation.

## Key findings

- Demonstrates convergence of Q-learning within the new framework
- Shows significant empirical benefits over traditional RL methods
- Extends Bellman operator to support broader control paradigms

## Abstract

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.