Chapter

Computational Learning Theory

Volume 2111 of the series Lecture Notes in Computer Science pp 589-604

Date:

Learning Rates for Q-Learning

  • Eyal Even-DarAffiliated withSchool of Computer Science, Tel-Aviv University
  • , Yishay MansourAffiliated withSchool of Computer Science, Tel-Aviv University

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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 the Q-learning. For a polynomial learning rate, one which is 1/t ω at time t where ω ε (1/2, 1), we show that 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 that this exponential behavior is inherent for a linear learning rate.