Regularized and Iterative Extensions of Feature Priming

Investigate whether regularized prime estimation, iterative or distribution-dependent feature-priming variants, and general randomized algorithms beyond the analyzed selectors and mixtures can achieve favorable online regret guarantees under the adversarial past-only protocol.

Background

The paper analyzes three one-stage feature-priming rules—univariate, Pearson, and multivariate least-squares priming—at a fixed power and with ridge regularization applied only to the transformed second-stage coefficient. Its lower bounds do not address regularizing the first-stage prime estimation, iterating the reweighting and refitting process, imposing distributional assumptions, or considering randomized algorithms more general than the specific selectors and mixtures studied.

These extensions are explicitly identified as unresolved because they could potentially alter the nuisance-interpolation mechanism responsible for the paper’s negative results, although no positive guarantee is conjectured or established for them.