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：我们开发了一个适用于非平稳环境下统计学习的通用框架。在每个时间段内，我们的方法应用稳定性原则来选择回顾窗口，该窗口在最大化历史数据利用率的同时，将累积偏差控制在相对于随机误差可接受的范围内。我们的理论展示了该方法对未知非平稳性的适应性。当总体损失函数为强凸或仅满足Lipschitz条件时，遗憾界在最小化最优性上达到对数因子内的最优。我们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划分为准平稳片段的分割技术。