### Abstract

Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension K and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is e-optimal from any initial state with high probability using Õ(K/ ^{2} (1 - γ) ^{3} ) sample transitions for arbitrarily large-scale MDP with a discount factor γ (0,1). A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to poly-log factors).

Original language | English (US) |
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Title of host publication | 36th International Conference on Machine Learning, ICML 2019 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 12095-12114 |

Number of pages | 20 |

ISBN (Electronic) | 9781510886988 |

State | Published - Jan 1 2019 |

Event | 36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States Duration: Jun 9 2019 → Jun 15 2019 |

### Publication series

Name | 36th International Conference on Machine Learning, ICML 2019 |
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Volume | 2019-June |

### Conference

Conference | 36th International Conference on Machine Learning, ICML 2019 |
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Country | United States |

City | Long Beach |

Period | 6/9/19 → 6/15/19 |

### All Science Journal Classification (ASJC) codes

- Education
- Computer Science Applications
- Human-Computer Interaction

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## Cite this

*36th International Conference on Machine Learning, ICML 2019*(pp. 12095-12114). (36th International Conference on Machine Learning, ICML 2019; Vol. 2019-June). International Machine Learning Society (IMLS).