Scalable LinUCB: Low-Rank Design Matrix Updates for Recommenders with Large Action Spaces

TL;DR

This paper presents PSI-LinUCB, a scalable and memory-efficient algorithm for large action space recommender systems that uses low-rank matrix updates and dynamical approximation to improve computational performance.

Contribution

We develop PSI-LinUCB, a novel scalable LinUCB variant employing low-rank updates and dynamical low-rank approximation for efficient large-scale recommendation tasks.

Findings

Effective in large recommender datasets

Reduced computational complexity to O(dr) per action

Maintains stable inverse matrix updates

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.