Scaling Up Q-Learning via Exploiting State–Action Equivalence

Recent success stories in reinforcement learning have demonstrated that leveraging structural properties of the underlying environment is key in devising viable methods capable of solving complex tasks. We study off-policy learning in discounted reinforcement learning, where some equivalence relation in the environment exists. We introduce a new model-free algorithm, called QL-ES (Q-learning with equivalence structure), which is a variant of (asynchronous) Q-learning tailored to exploit the equivalence structure in the MDP. We report a non-asymptotic PAC-type sample complexity bound for QL-ES, thereby establishing its sample efficiency. This bound also allows us to quantify the superiority of QL-ES over Q-learning analytically, which shows that the theoretical gain in some domains can be massive. We report extensive numerical experiments demonstrating that QL-ES converges significantly faster than (structure-oblivious) Q-learning empirically. They imply that the empirical performance gain obtained by exploiting the equivalence structure could be massive, even in simple domains. To the best of our knowledge, QL-ES is the first provably efficient model-free algorithm to exploit the equivalence structure in finite MDPs.