A Stability Principle for Learning Under Nonstationarity
Chengpiao Huang, Kaizheng Wang
Operations Research · 2025 · Volume 73 · Issue 6
Abstract
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. Funding: This work was supported by the Data Science Institute, Columbia University [Seed Grant SF-181], the National Science Foundation [Grant DMS-2210907], and Fu Foundation School of Engineering and Applied Science (startup grant). Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results are available at https://doi.org/10.1287/opre.2024.0766 .
Keywords
Machine Learning and Data Science, nonstationarity, online learning, distribution shift, adaptivity, look-back window
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