Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.08779
- arXiv:
- arXiv:1901.08779
- Bibcode:
- 2019arXiv190108779Z
- Keywords:
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- Computer Science - Machine Learning;
- Statistics - Machine Learning