arXiv Machine Learning

Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates

The paper investigates online linear regression with sparse comparators, focusing on feature priming techniques that reweight features using past data. It establishes sparse‑regret lower bounds that invalidate sparse‑logarithmic guarantees for univariate, Pearson, and multivariate priming rules under a past‑only Moore–Penrose protocol, showing ≥Ω(min{T,√d}) clipped regret for unit‑power rules and linear regret for powered rules in high dimensions. The authors also provide tight rank upper bounds for certain priming schemes and present algebraic constructions yielding Ω(min{T,d^{1/4}}) regret for unit‑power multivariate priming, while noting that the exact multivariate frontier remains open.

arXiv Machine Learning
Aug 19

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

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.

By Huibo Xu, Shi Fu, Qixin Zhang, Dacheng Tao
arXiv Machine Learning
Sep 10

High-dimensional Linear Bandits with Knapsacks

The paper studies high‑dimensional linear contextual bandits with knapsack constraints (CBwK), aiming to exploit sparsity for tighter regret bounds. It introduces an online hard‑thresholding estimator integrated into a primal‑dual framework, achieving sub‑linear regret that grows only logarithmically with the feature dimension. Under either a diverse‑covariate or margin condition, the regret improves to τ‑dependent rates, and when both hold simultaneously, a dual resolving scheme yields an even tighter bound. The approach also recovers optimal rates for high‑dimensional contextual bandits without knapsacks, and experiments demonstrate its practical effectiveness.

By Wanteng Ma, Dong Xia, Jiashuo Jiang
arXiv Machine Learning
Aug 10

Multiscale Reward Hedging from Correct Demonstrations

arXiv:2608. 06825v1 Announce Type: new Abstract: Learning from correct demonstrations is harder than supervised learning when many answers are correct: after predicting, the learner sees one valid answer but not whether its own answer was valid, nor any reward.

By Pahan Dewasurendra
arXiv Machine Learning
Aug 12

High-Dimensional Calibration from Swap Regret

arXiv:2505. 21460v2 Announce Type: replace Abstract: We study online calibration of multi-dimensional forecasts over an arbitrary convex set $P \subset \mathbb{R}^d$ relative to an arbitrary norm $|\cdot|$.

By Maxwell Fishelson, Noah Golowich, Mehryar Mohri, Jon Schneider
arXiv Machine Learning
Aug 28

Privacy Without Regret: Differentially Private Inference-Time Alignment

The paper introduces Private Best-of-N (PrivBoN), a method that adds calibrated Gumbel noise to reward scores during inference-time alignment, achieving both ε-differential privacy and KL-regularized alignment. When the privacy budget exceeds a critical threshold ε*, the noise becomes regret-optimal, matching the theoretical alignment skyline. The authors also propose Private Inference-Time Pessimism (PrivITP), which uses χ^2-regularized rejection sampling and a two-phase Gaussian mechanism to provide ex-post (ε,δ)-DP with a privacy cost independent of the number of responses, and demonstrate that both methods outperform standard Best-of-N across multiple models and datasets.

By Ishi Jain, Nandini Bhattad, Sayak Ray Chowdhury