Chris Watkins   Peter Dayan
Machine Learning, 8, 279-292.
Q-learning (Watkins, 1989) is a simple way for agents to learn how to
act optimally in controlled Markovian domains. It amounts to an
incremental method for dynamic programming which imposes limited
computational demands. It works by successively improving its evaluations
of the quality of particular actions at particular states. The paper
presents and proves in detail a convergence theorem for Q-learning. It
shows that Q-learning converges to the optimum action-values with
probability 1 so long as all actions are repeatedly sampled in all states
and the action-values are represented discretely. Extensions to the cases
of nondiscounted, but absorbing, Markov environments, and where many Q
values can be changed each iteration, rather than just one.