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arXiv · 2002.03580

Combinatorial Semi-Bandit in the Non-Stationary Environment

Wei Chen·Liwei Wang·Haoyu Zhao·Kai Zheng
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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.

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BibTeXRIS

Wei Chen, Liwei Wang, Haoyu Zhao, Kai Zheng. 2020-02-10. Combinatorial Semi-Bandit in the Non-Stationary Environment. https://arxiv.org/abs/2002.03580

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