## Abstract

We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors. It enjoys an O^{e}(H^{2.5p}T|S||A|(R_{TH}(O) + H log(δ^{−1}))) regret guarantee, with T being the number of episodes, S the state space, A the action space, H the horizon and R_{TH}(O) = R_{TH}(O_{sq}^{F} ) + R_{TH}(O_{log}^{P} ) is the sum of the square and log-loss regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient rate optimal regret minimization algorithm for adversarial CMDPs that operates under the minimal standard assumption of online function approximation.

Original language | English |
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Pages (from-to) | 19287-19314 |

Number of pages | 28 |

Journal | Proceedings of Machine Learning Research |

Volume | 202 |

State | Published - 2023 |

Event | 40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States Duration: 23 Jul 2023 → 29 Jul 2023 |

### Funding

Funders | Funder number |
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Yandex Initiative for Machine Learning | |

Horizon 2020 Framework Programme | |

Blavatnik Family Foundation | |

European Research Council | |

Israel Science Foundation | 2250/22 |

Israel Science Foundation | |

Tel Aviv University | |

Horizon 2020 | 2549/19, 882396, 993/17 |

Horizon 2020 |