{"ID":2851590,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.19349","arxiv_id":"2510.19349","title":"Scalable LinUCB: Low-Rank Design Matrix Updates for Recommenders with Large Action Spaces","abstract":"In this paper, we introduce PSI-LinUCB, a scalable variant of LinUCB that enables efficient training, inference, and memory usage by representing the inverse regularized design matrix as a sum of a diagonal matrix and low-rank correction. We derive numerically stable rank-1 and batched updates that maintain the inverse without explicitly forming the matrix. To control memory growth, we employ a projector-splitting integrator for dynamical low-rank approximation, yielding an average per-step update cost and memory usage of $O(dr)$ for approximation rank $r$. The inference complexity of the proposed algorithm is $O(dr)$ per action evaluation. Experiments on recommender system datasets demonstrate the effectiveness of our algorithm.","short_abstract":"In this paper, we introduce PSI-LinUCB, a scalable variant of LinUCB that enables efficient training, inference, and memory usage by representing the inverse regularized design matrix as a sum of a diagonal matrix and low-rank correction. We derive numerically stable rank-1 and batched updates that maintain the inverse...","url_abs":"https://arxiv.org/abs/2510.19349","url_pdf":"https://arxiv.org/pdf/2510.19349v2","authors":"[\"Evgenia Shustova\",\"Marina Sheshukova\",\"Sergey Samsonov\",\"Evgeny Frolov\"]","published":"2025-10-22T08:17:42Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}