## Learning Rates for Q-learning

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Eyal Even-Dar, Yishay Mansour**; 5(Dec):1--25, 2003.

### Abstract

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*

^{ω}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 which is 1/

*t*at time

*t*, the convergence rate has an exponential dependence on 1/(1-γ). In addition we show a simple example that proves this exponential behavior is inherent for linear learning rates.