{"ID":2829044,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13506","arxiv_id":"2512.13506","title":"Learning under Distributional Drift: Prequential Reproducibility as an Intrinsic Statistical Resource","abstract":"Statistical learning under distributional drift remains poorly characterized, especially in closed-loop settings where learning alters the data-generating law. We introduce an intrinsic drift budget $C_T$ that quantifies cumulative information-geometric motion of the data distribution along the realized learner-environment trajectory, measured in Fisher-Rao distance. The budget separates exogenous environmental change from policy-sensitive feedback induced by the learner's actions. This gives a rate-based characterization of prequential reproducibility: when performance on the realized stream is used to predict one-step-ahead performance under the next distribution, the drift contribution enters through the average motion rate $C_T/T$, not through cumulative drift alone. We prove a drift-feedback bound of order $T^{-1/2}+C_T/T$, up to controlled second-order remainder terms, and establish a matching sharpness lower bound for the same prequential reproducibility gap on a canonical regular subclass. Thus the dependence on the average Fisher-Rao motion rate is tight up to constants: $C_T/T$ is sufficient for upper control and unavoidable on regular hard subclasses. We further prove an information-theoretic indistinguishability result showing that order-$C/T$ effects on the one-step-ahead target need not be identifiable from the realized performance stream alone. Finally, we show that fixed monitoring channels induce contracted observable Fisher motion, and experiments, including a misspecified real-data feedback setting, indicate that appropriately chosen channels can retain risk-relevant drift signal when the intrinsic data-generating law is unavailable. The resulting theory treats exogenous drift, adaptive data analysis, and performative feedback as different sources of Fisher-Rao motion along the same learner-environment trajectory.","short_abstract":"Statistical learning under distributional drift remains poorly characterized, especially in closed-loop settings where learning alters the data-generating law. We introduce an intrinsic drift budget $C_T$ that quantifies cumulative information-geometric motion of the data distribution along the realized learner-environ...","url_abs":"https://arxiv.org/abs/2512.13506","url_pdf":"https://arxiv.org/pdf/2512.13506v4","authors":"[\"Sofiya Zaichyk\"]","published":"2025-12-15T16:34:47Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}