Fast Rates for Nonstationary Weighted Risk Minimization
Read the original on arXiv Machine Learning →The paper investigates weighted empirical risk minimization under nonstationary data, decomposing the excess risk into a learning component and a drift component. It establishes oracle inequalities for the learning error under mixing conditions, uniformly over arbitrary weight classes, and derives explicit bounds for drift errors in square loss settings, covering structural‑break and smoothly drifting processes. The analysis is extended to auto‑regression problems with linear models, basis approximations, and neural networks, revealing that optimal weights balance learning and drift via a bias–variance trade‑off and recover minimax‑optimal rates in unweighted, stationary cases.
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