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 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\big(\log(n)/(\epsilon {2}(1-\gamma) {4})\big) 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.

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\big(\log(n)/(\epsilon {2}(1-\gamma) {4})\big) 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. Papers published at the Neural Information Processing Systems Conference.

In this paper, we derive a generalization of the Speedy Q-learning (SQL) algorithm that was proposed in the Reinforcement Learning (RL) literature to handle slow convergence of Watkins' Q-learning. In most RL algorithms such as Q-learning, the Bellman equation and the Bellman operator play an important role. It is possible to generalize the Bellman operator using the technique of successive relaxation. We use the generalized Bellman operator to derive a simple and efficient family of algorithms called Generalized Speedy Q-learning (GSQL-w) and analyze its finite time performance. We show that GSQL-w has an improved finite time performance bound compared to SQL for the case when the relaxation parameter w is greater than 1. This improvement is a consequence of the contraction factor of the generalized Bellman operator being less than that of the standard Bellman operator. Numerical experiments are provided to demonstrate the empirical performance of the GSQL-w algorithm.

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\big(\log(n)/(\epsilon^{2}(1-\gamma)^{4})\big) 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.