### Abstract

We consider fixed step-size Q-learning algorithms applied to finite state and action space, discounted reward Markov decision problems (MDPs). In previous work we derived a bound on the first moment of the Q-value estimation error, specifically on the expected steady-state value of the infinity norm of the error. The goal in both this paper, and the previous, is to maximize a discounted sum of rewards over an infinite time horizon. However, in our previous work, the bound we derived holds only when the step-size is sufficiently, and sometimes impractically, small. In this paper, we present a new error bound that, as before, goes to zero as the step-size goes to zero, but is also valid for all values of the step-size. To obtain the new bound, we divide time into frames such that the probability that there is some state that is not visited within the frame is strictly less than 1: Our error bound is then found by sampling the system one time in every frame.

Original language | English (US) |
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Title of host publication | 2013 American Control Conference, ACC 2013 |

Pages | 1926-1931 |

Number of pages | 6 |

State | Published - 2013 |

Event | 2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013 |

### Other

Other | 2013 1st American Control Conference, ACC 2013 |
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Country | United States |

City | Washington, DC |

Period | 6/17/13 → 6/19/13 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*2013 American Control Conference, ACC 2013*(pp. 1926-1931). [6580117]