In this paper we derive convergence rates for Q-learning. We show an interesting relationship between the convergence rate and the learning rate used in Q-learning. For a polynomial learning rate, one which is 1/t at time t where ω ∈ (1/2, 1), we show that the convergence rate is polynomial in 1/(1− γ), where γ is the discount factor. In contrast we show that for a linear learning rate, one whi...