A Stability Principle for Learning Under Nonstationarity

• 成果类型: Article; Early Access
• 署名作者: Huang, Chengpiao; Wang, Kaizheng
• 署名单位: Columbia University; Columbia University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0766
• 发表日期: 2025
• 关键词: change-point detection

摘要

We develop a versatile framework for statistical learning in nonstationary 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 adaptivity of this approach to unknown nonstationarity. We prove regret bounds that are 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 nonstationary data sequence into quasistationary pieces. We evaluate the practical performance of our approach through real-data experiments on electricity demand prediction and hospital nurse staffing.