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      Combinatorial multi-armed bandit problem with probabilistically triggered arms: a case with bounded regret

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      Author
      Sarıtaç, A. Ömer
      Tekin, Cem
      Date
      2017-11
      Source Title
      2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
      Publisher
      IEEE
      Pages
      111 - 115
      Language
      English
      Type
      Conference Paper
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      Abstract
      In this paper, we study the combinatorial multi-armed bandit problem (CMAB) with probabilistically triggered arms (PTAs). Under the assumption that the arm triggering probabilities (ATPs) are positive for all arms, we prove that a simple greedy policy, named greedy CMAB (G-CMAB), achieves bounded regret. This improves the result in previous work, which shows that the regret is O (log T) under no such assumption on the ATPs. Then, we numerically show that G-CMAB achieves bounded regret in a real-world movie recommendation problem, where the action corresponds to recommending a set of movies, arms correspond to the edges between movies and users, and the goal is to maximize the total number of users that are attracted by at least one movie. In addition to this problem, our results directly apply to the online influence maximization (OIM) problem studied in numerous prior works.
      Keywords
      Bounded regret
      Combinatorial multi-armed bandit
      Online learning
      Probabilistically triggered arms
      Permalink
      http://hdl.handle.net/11693/50176
      Published Version (Please cite this version)
      https://doi.org/10.1109/GlobalSIP.2017.8308614
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      • Department of Electrical and Electronics Engineering 3597
      • Department of Industrial Engineering 684
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