Abstract

We introduce a new convergent variant of Q-learning, called speedy Q-learning (SQL), to address the problem of slow convergence in the standard form of the Q-learning algorithm. We prove a PAC bound on the performance of SQL, which
n state-action pairs and the discount factor only T = steps are required for the SQL algorithm to converge to an optimal action-value function with high probability. This bound has a better dependency on and thus, is tighter than the best available result for Q-learning. Our bound is also superior to the existing results for both modelfree and model-based instances of batch Q-value iteration that are considered to be more efficient than the incremental methods like Q-learning.