We consider the problem of prediction with expert advice for ``easy'' sequences. We show that a variant of NormalHedge enjoys a second-order $ε$-quantile regret bound of $O\big(\sqrt{V_T \log(V_T/ε)}\big) $ when $V_T > \log N$, where $V_T$ is the cumulative second moment of instantaneous per-expert regret averaged with respect to a natural distribution determined by the algorithm. The algorithm is motivated by a continuous time limit using Stochastic Differential Equations. The discrete time analysis uses self-concordance techniques.

翻译：本文研究"简单"序列的专家预测问题。我们证明NormalHedge的变体在$V_T > \log N$时具有$O\big(\sqrt{V_T \log(V_T/ε)}\big)$的二阶$ε$-分位数遗憾界，其中$V_T$表示瞬时单专家遗憾的累积二阶矩，该矩按算法确定的自然分布进行加权平均。该算法通过随机微分方程的连续时间极限推导得到。离散时间分析采用自协调技术实现。