Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates
In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore--Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insuffic...
| Authors | Huibo Xu, Shi Fu, Qixin Zhang et al. |
|---|---|
| Primary category | stat.ML |
| Published | 18 August 2026 |
| Last updated at source | 7 September 2026 |
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