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 for approximation rank . The inference complexity of the proposed algorithm is per action evaluation. Experiments on recommender system datasets demonstrate the effectiveness of our algorithm.