自归一化Bernstein不等式扩展到再生过程，适用于非独立同分布数据学习
Self-normalized Bernstein Inequalities for Regenerative Processes and Applications to Learning Without Independence
一篇纯理论论文，把Bernstein不等式推广到再生过程，让泛化误差界不再依赖独立同分布假设，还给出了极小化最优性证明。
论文为具有独立同分布标记循环的再生过程证明了自归一化Bernstein不等式，界中使用观测到的循环长度，并显式处理截断与超出观测范围的末尾循环。从有限确定集合中选取调节参数可得到一项除再生时间尾部外均为经验项的Bernstein不等式，且该剩余项在许多感兴趣的情形下是二阶的。作者由此推导了非独立同分布再生数据下分类问题的泛化误差界，并通过最小化一阶项定义仍满足oracle不等式的不可知分类器。该平均偏差界在样本量和期望再生时间上被证明是极小化最优的，结合再生强近似还可得到基于可观测块方差估计的高斯近似。
Self-normalized Bernstein Inequalities for Regenerative Processes and Applications to Learning Without Independence
We prove a self-normalized Bernstein inequality for bounded functions of a regenerative process with independent, identically distributed marked cycles of finite mean length. The bound uses observed cycle lengths and retains explicit terms for truncation and the cycle ending after the observation horizon. Selecting a tuning parameter from a finite deterministic collection gives a version of Bernstein inequality where all terms are empirical but one, related to the tails of the regeneration times. We then study this term in many regimes: it turns out that it is of second-order in many cases of interest. This is important for applications in machine learning: we prove generalization error bounds for classification with non-i.i.d., regenerative data. These bounds can be used to define learning objectives: by minimizing the first-order term only in the bound, we define agnostic classifiers that still satisfy oracle inequalities. We also show that the bound on the average deviation provided by our results is minimax-optimal in the sample size and in the expected regeneration time. Finally, we combine the Bernstein inequality with a regenerative strong approximation to obtain a Gaussian approximation using an observable block variance estimator.