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arXiv · 1901.08779

Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously

Julian Zimmert·Haipeng Luo·Chen-Yu Wei
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Abstract

We develop the first general semi-bandit algorithm that simultaneously achieves $\mathcal{O}(\log T)$ regret for stochastic environments and $\mathcal{O}(\sqrt{T})$ regret for adversarial environments without knowledge of the regime or the number of rounds $T$. The leading problem-dependent constants of our bounds are not only optimal in some worst-case sense studied previously, but also optimal for two concrete instances of semi-bandit problems. Our algorithm and analysis extend the recent work of (Zimmert & Seldin, 2019) for the special case of multi-armed bandit, but importantly requires a novel hybrid regularizer designed specifically for semi-bandit. Experimental results on synthetic data show that our algorithm indeed performs well uniformly over different environments. We finally provide a preliminary extension of our results to the full bandit feedback.

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Julian Zimmert, Haipeng Luo, Chen-Yu Wei. 2019-01-25. Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously. https://arxiv.org/abs/1901.08779

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