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arXiv Statistics ML By Tobias Brock, Thomas Nagler

Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization

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The paper studies distributional drift in nonstationary weighted risk minimization by breaking down excess risk into estimation, drift, and approximation parts. It argues that traditional discrepancy-based bounds are often overly conservative because they can scale larger than the actual excess-risk contribution and react to risk surface changes that do not affect the optimal predictor. The authors provide a tighter oracle drift bound, analyze its behavior in parametrized regression models—particularly linear regression—and extend the results to nonparametric regression.

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