Corruption-Robust Sparse Linear Contextual Bandits with Knapsack Constraints

2026-09-29

AI Summary

This study addresses the challenging resource allocation problem in sparse linear contextual bandits with knapsack constraints under dual contamination of both rewards and consumptions. To tackle this, we propose the ROPD framework, which integrates contamination-robust confidence intervals, online resource pricing, and budget-safety rules. This work provides the first coupled analysis of consumption contamination within statistical estimation and budget accounting, alongside a shared grid mechanism designed to adapt to unknown contamination levels. Leveraging primal-dual optimization and sparse estimation, the proposed approach achieves sublinear regret bounds while rigorously preserving observational budget integrity, effectively mitigating resource violations induced by cumulative consumption contamination.

Abstract

We study sparse linear contextual bandits with knapsack constraints under joint reward and consumption corruption. Consumption corruption creates a challenge beyond corrupted rewards: it affects not only statistical estimates, but also the recorded budget, resource prices, and stopping decisions that govern future allocation. We develop Robust Optimistic Primal--Dual (ROPD), an estimator-modular framework that combines corruption-aware confidence widths with online resource prices and a budget-safety rule. With concrete sparse implementation, ROPD achieves regret against a clean population-LP benchmark of $\widetilde O(T^{2/3}+ΓT^{1/3})$ under forced exploration and population-design coverage, and $\widetilde O(\sqrt T+Γ)$ under on-policy realized-design coverage, for a supplied valid corruption bound $Γ$ under the stated proportional-budget scaling and fixed model/design parameters. When the corruption level is unknown, Shared-Grid adapts confidence radii around common point estimates fitted to a single realized history, incurring explicit initialization and master-comparison costs; its sharper on-policy guarantee additionally requires recommendation coverage. Both methods preserve observed budgets on every realization and bound clean resource violation by cumulative consumption corruption. These results connect corruption-robust sparse estimation with resource accounting, pricing, and stopping in high-dimensional online allocation.

Problem

• contextual bandits
• knapsack constraints
• corruption-robust
• sparse linear models
• resource allocation

Innovation

• Corruption-Robust
• Sparse Linear Contextual Bandits
• Knapsack Constraints
• Primal-Dual Framework
• Online Resource Allocation