  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.
