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Thompson Sampling for Combinatorial Semi-bandits with Sleeping Arms and Long-Term Fairness Constraints | | Zhiming Huang
; Yifan Xu
; Bingshan Hu
; Qipeng Wang
; Jianping Pan
; | | Date: |
14 May 2020 | | Abstract: | We study the combinatorial sleeping multi-armed semi-bandit problem with
long-term fairness constraints~(CSMAB-F). To address the problem, we adopt
Thompson Sampling~(TS) to maximize the total rewards and use virtual queue
techniques to handle the fairness constraints, and design an algorithm called
emph{TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B)}.
Further, we prove TSCSF-B can satisfy the fairness constraints, and the
time-averaged regret is upper bounded by $frac{N}{2eta} +
Oleft(frac{sqrt{mNTln T}}{T}
ight)$, where $N$ is the total number of
arms, $m$ is the maximum number of arms that can be pulled simultaneously in
each round~(the cardinality constraint) and $eta$ is the parameter trading off
fairness for rewards. By relaxing the fairness constraints (i.e., let $eta
ightarrow infty$), the bound boils down to the first problem-independent
bound of TS algorithms for combinatorial sleeping multi-armed semi-bandit
problems. Finally, we perform numerical experiments and use a high-rating movie
recommendation application to show the effectiveness and efficiency of the
proposed algorithm. | | Source: | arXiv, 2005.6725 | | Services: | Forum | Review | PDF | Favorites | |
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