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arXiv Machine Learning By Huibo Xu, Shi Fu, Qixin Zhang, Dacheng Tao

Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and a Tight Univariate Rate

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The paper investigates feature priming in high‑dimensional online linear regression, showing that estimating feature weights from past data and refitting a minimum‑norm predictor can lead to regret that scales with sparsity rather than ambient dimension. It provides a negative answer to a COLT 2023 open problem by proving that three natural priming rules incur ≥Ω(min{T,√d}) regret against a zero‑loss one‑sparse comparator, due to cheap nuisance interpolation that underweights truly predictive coordinates. The authors also identify conditions under which regret is governed by data rank and present constructions that achieve tight univariate rates, while noting that the multivariate case remains unresolved.

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