Corruption-Robust Sparse Linear Contextual Bandits with Knapsack Constraints

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 $\widetilde O(T^{2/3}+\Gamma T^{1/3})$ under forced exploration and population-design coverage, and $\widetilde O(\sqrt T+\Gamma)$ under on-policy realized-design coverage, for a supplied valid corruption bound $\Gamma$ 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.

Machine Learning (cs.LG)

arXiv:2609.37189 [cs.LG]

(or arXiv:2609.37189v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.37189 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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