Title: The Price of Adapting to Multiple Structural Shifts

Abstract: This study investigates online learning within environments characterized by multiple change points. While the single change point scenario has been extensively analyzed using traditional "high confidence" detection frameworks, the presence of multiple shifts introduces distinct theoretical and algorithmic hurdles. We demonstrate that conventional approaches can suffer from severe performance degradation—manifesting as high regret—due to a phenomenon identified as endogenous confounding. To address this, we introduce Anytime Tracking CUSUM (ATC), a novel family of learning algorithms. These are horizon-free methods that employ a selective detection strategy, designed to disregard minor, difficult-to-detect fluctuations while responding rapidly to substantial changes. We establish that a well-calibrated ATC algorithm achieves performance that is nearly minimax-optimal; specifically, its regret aligns closely with a new information-theoretic lower bound defining the best possible performance for any algorithm in this multiple change point context. Our theoretical results are corroborated by experiments conducted on both synthetic and real-world datasets.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC