Online Reinforcement Learning of Optimal Threshold Policies for Markov Decision Processes

Arghyadip Roy, Vivek S. Borkar, Abhay Karandikar, Prasanna Chaporkar

Abstract: To overcome the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">curses of dimensionality and modeling</i> of dynamic programming methods to solve Markov decision process problems, reinforcement learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms, which do not consider the structural properties of the optimal policy, we propose a structure-aware learning algorithm to exploit the ordered multithreshold structure of the optimal policy, if any. We prove the asymptotic convergence of the proposed algorithm to the optimal policy. Due to the reduction in the policy space, the proposed algorithm provides remarkable improvements in storage and computational complexities over classical RL algorithms. Simulation results establish that the proposed algorithm converges faster than other RL algorithms.