Mirror descent with an entropic regularizer is known to achieve shifting
regret bounds that are logarithmic in the dimension. This is done using either
a carefully designed projection or by a weight sharing technique. Via a novel
unified analysis, we show that these two approaches deliver essentially
equivalent bounds on a notion of regret generalizing shifting, adaptive,
discounted, and other related regrets. Our analysis also captures and extends
the generalized weight sharing technique of Bousquet and Warmuth, and can be
refined in several ways, including improvements for small losses and adaptive
tuning of parameters.

研究使用镜像下降和熵正则化的方法在维度上实现对于一系列的一般化后的后悔情况的误差上界，其中包括了位移、自适应、折扣等等，并且得到了和权值分享方法的等价结果。研究同时提出了对于小的误差和参数的自适应调整等的改进。

镜面下降遇见固定分配 (无悔感)

Mirror Descent Meets Fixed Share (and feels no regret)

We show that for a general class of convex online learning problems, Mirror
Descent can always achieve a (nearly) optimal regret guarantee.

对于一般的凸在线学习问题，我们证明镜像下降法总是可以实现（几乎）最优的遗憾保证。