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.

References

Regularized prime estimation, iterative or distribution-dependent variants, and general randomized algorithms beyond the stated switchers and mixtures remain open.

— Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and a Tight Univariate Rate  (2608.17573 - Xu et al., 18 Aug 2026) in Section 1, Introduction

The regret analysis for LP-Chain is left for future work.

— AFA-BANDIT: Provably Near-Optimal Online Multi-Feature Classification Under Budget Constraints  (2610.07615 - Odeh et al., 6 Oct 2026) in Section 4, Regret Analysis

Our lower bounds match our upper bounds up to logarithmic factors in the stated coverage regimes (see \Cref{def:spectral-coverage-regimes}), but we do not obtain matching bounds for arbitrary offline coverage.

— Gaussian-Width Bounds for Offline-to-Online Linear Bandits  (2610.12990 - Chandak et al., 9 Oct 2026) in Section 6, “Conclusion”