## Abstract

We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for each agent v an individual expected regret of O^{e} (r( 1 + _{|N}^{K}_{(}v)_{|} ) T ), where T is the number of time steps, K is the number of actions and N (v) is the set of neighbors of agent v in the communication graph. We present algorithms both for the case that the communication graph is known to all the agents, and for the case that the graph is unknown. When the graph is unknown, each agent knows only the set of its neighbors and an upper bound on the total number of agents. The individual regret between the models differs only by a logarithmic factor. Our work resolves an open problem from [Cesa-Bianchi et al., 2019b].

Original language | English |
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Journal | Advances in Neural Information Processing Systems |

Volume | 32 |

State | Published - 2019 |

Event | 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada Duration: 8 Dec 2019 → 14 Dec 2019 |

### Funding

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

Israel Science Foundation |