### Abstract

Bandit is a framework for designing sequential experiments, where a learner selects an arm A ϵ A and obtains an observation corresponding to A in each experiment. Theoretically, the tight regret lower-bound for the general bandit is polynomial with respect to the number of arms |A|, and thus, to overcome this bound, the bandit problem with side-information is often considered. Recently, a bandit framework over a causal graph was introduced, where the structure of the causal graph is available as side-information and the arms are identified with interventions on the causal graph. Existing algorithms for causal bandit overcame the Ω(√\A\/T) simple-regret lower-bound; however, their algorithms work only when the interventions A are localized around a single node (i.e., an intervention propagates only to its neighbors). We then propose a novel causal bandit algorithm for an arbitrary set of interventions, which can propagate throughout the causal graph. We also show that it achieves O(√γ^{∗} log(|A|T)/T) regret bound, where γ^{∗} is determined by using a causal graph structure. In particular, if the maximum in-degree of the causal graph is a constant, then γ^{∗} = O(N^{2}), where N is the number of nodes.

Original language | English |
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Title of host publication | 35th International Conference on Machine Learning, ICML 2018 |

Editors | Jennifer Dy, Andreas Krause |

Publisher | International Machine Learning Society (IMLS) |

Pages | 8761-8781 |

Number of pages | 21 |

ISBN (Electronic) | 9781510867963 |

Publication status | Published - 2018 Jan 1 |

Event | 35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden Duration: 2018 Jul 10 → 2018 Jul 15 |

### Publication series

Name | 35th International Conference on Machine Learning, ICML 2018 |
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Volume | 12 |

### Other

Other | 35th International Conference on Machine Learning, ICML 2018 |
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Country | Sweden |

City | Stockholm |

Period | 18/7/10 → 18/7/15 |

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Human-Computer Interaction
- Software

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## Cite this

*35th International Conference on Machine Learning, ICML 2018*(pp. 8761-8781). (35th International Conference on Machine Learning, ICML 2018; Vol. 12). International Machine Learning Society (IMLS).