Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions

Kei Takemura, Shinji Ito, Daisuke Hatano, Hanna Sumita, Takuro Fukunaga, Naonori Kakimura, Ken Ichi Kawarabayashi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of rewards of arms. Several existing algorithms have regret bounds that are optimal with respect to the number of rounds T. However, there is a gap of Õ(max(d, k)) between the current best upper and lower bounds, where d is the dimension of the feature vectors, k is the number of the chosen arms in a round, and Õ(·) ignores the logarithmic factors. The dependence of k and d is of practical importance because k may be larger than T in real-world applications such as recommender systems. In this paper, we fill the gap by improving the upper and lower bounds. More precisely, we show that the C2UCB algorithm proposed by Qin, Chen, and Zhu (2014) has the optimal regret bound Õ(d√kT + dk) for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C2UCB algorithm and demonstrate that it enjoys the optimal regret bound for a more general problem that can take into account other objectives simultaneously. We also show that our technique would be applicable to related problems. Numerical experiments support our theoretical results and considerations.

Original languageEnglish
Title of host publication35th AAAI Conference on Artificial Intelligence, AAAI 2021
PublisherAssociation for the Advancement of Artificial Intelligence
Pages9791-9798
Number of pages8
ISBN (Electronic)9781713835974
Publication statusPublished - 2021
Event35th AAAI Conference on Artificial Intelligence, AAAI 2021 - Virtual, Online
Duration: 2021 Feb 22021 Feb 9

Publication series

Name35th AAAI Conference on Artificial Intelligence, AAAI 2021
Volume11A

Conference

Conference35th AAAI Conference on Artificial Intelligence, AAAI 2021
CityVirtual, Online
Period21/2/221/2/9

ASJC Scopus subject areas

  • Artificial Intelligence

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