Mohammad Gheshlaghi Azar, Remi Munos, Mohammad Ghavamzadeh and Hilbert Kappen
In: Twenty-Fifth Annual Conference on Advances in Neural Information Processing Systems (NIPS-2011), Granada, Spain(2011).
We introduce a new convergent variant of Q-learning, called speedy Q-learning, 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 shows that for an MDP with n state-action pairs and the discount factor \gamma only T = O(log(n)/(\epsilon^2(1 − \gamma)^4)) steps are required for the SQL algorithm to converge to an \epsilon-optimal action-value function with high probability. This bound has a better dependency on 1/\epsilon and 1/(1−\gamma), and thus, is tighter than the best available result for Q-learning. Our bound is also superior to the existing results for both model- free and model-based instances of batch Q-value iteration that are considered to be more efficient than the incremental methods like Q-learning.