We develop a novel and generic algorithm for the adversarial multi-armed bandit problem (or more generally the combinatorial semi-bandit problem). When instantiated differently, our algorithm achieves various new data-dependent regret bounds improving previous works. Examples include: 1) a regret bound depending on the variance of only the best arm; 2) a regret bound depending on the first-order path-length of only the best arm; 3) a regret bound depending on the sum of first-order path-lengths of all arms as well as an important negative term, which together lead to faster convergence rates for some normal form games with partial feedback; 4) a regret bound that simultaneously implies small regret when the best arm has small loss and logarithmic regret when there exists an arm whose expected loss is always smaller than those of others by a fixed gap (e.g. the classic i.i.d. setting). In some cases, such as the last two results, our algorithm is completely parameter-free. The main idea of our algorithm is to apply the optimism and adaptivity techniques to the well-known Online Mirror Descent framework with a special log-barrier regularizer. The challenges are to come up with appropriate optimistic predictions and correction terms in this framework. Some of our results also crucially rely on using a sophisticated increasing learning rate schedule.

提出了一种新颖的算法，采用乐观性和适应性技术，结合在线镜像下降框架和特殊的对数障碍正则化器来解决对抗性多臂赌博机问题和组合半赌博问题，并在提高先前工作的同时，取得了多种新的数据依赖性遗憾界。

更多适应性算法用于对抗式赌博机