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Combinatorial Semi-Bandit in the Non-Stationary Environment

Wei Chen,Liwei Wang,Haoyu Zhao

Published 2020 in Conference on Uncertainty in Artificial Intelligence

ABSTRACT

In this paper, we investigate the non-stationary combinatorial semi-bandit problem, both in the switching case and in the dynamic case. In the general case where (a) the reward function is non-linear, (b) arms may be probabilistically triggered, and (c) only approximate offline oracle exists \cite{wang2017improving}, our algorithm achieves $\tilde{\mathcal{O}}(\sqrt{\mathcal{S} T})$ distribution-dependent regret in the switching case, and $\tilde{\mathcal{O}}(\mathcal{V}^{1/3}T^{2/3})$ in the dynamic case, where $\mathcal S$ is the number of switchings and $\mathcal V$ is the sum of the total ``distribution changes''. The regret bounds in both scenarios are nearly optimal, but our algorithm needs to know the parameter $\mathcal S$ or $\mathcal V$ in advance. We further show that by employing another technique, our algorithm no longer needs to know the parameters $\mathcal S$ or $\mathcal V$ but the regret bounds could become suboptimal. In a special case where the reward function is linear and we have an exact oracle, we design a parameter-free algorithm that achieves nearly optimal regret both in the switching case and in the dynamic case without knowing the parameters in advance.

PUBLICATION RECORD

  • Publication year

    2020

  • Venue

    Conference on Uncertainty in Artificial Intelligence

  • Publication date

    2020-02-10

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 2002.03580
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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