We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while keeping the cumulative bias within an acceptable range relative to the stochastic error. Our theory showcases the adaptability of this approach to unknown non-stationarity. The regret bound is minimax optimal up to logarithmic factors when the population losses are strongly convex, or Lipschitz only. At the heart of our analysis lie two novel components: a measure of similarity between functions and a segmentation technique for dividing the non-stationary data sequence into quasi-stationary pieces.

翻译：我们提出了一种适用于非平稳环境下统计学习的通用框架。在每个时间周期内，我们的方法基于稳定性原则选择回顾窗口，在使累积偏差相对于随机误差控制在可接受范围内的同时，最大化历史数据的利用效率。理论分析表明该方法能够自适应于未知的非平稳性。当总体损失函数满足强凸性或仅满足Lipschitz条件时，该方法的遗憾界在忽略对数因子后达到极小化最优。分析的核心包含两个创新要素：函数间的相似性度量以及将非平稳数据序列分割为准平稳片段的切分技术。