  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.
