针对大规模推荐系统，提出低秩更新的可扩展线性算法
Scalable LinUCB: Low-Rank Design Matrix Updates for Recommenders with Large Action Spaces
- 用对角+低秩形式表示逆设计矩阵，避免显式计算
- 每步更新和内存开销为O(dr)，支持高效推理
- 适合高动作空间推荐场景，尤其资源受限时
本文提出PSI-LinUCB，一种可扩展的LinUCB变体，通过将正则化设计矩阵的逆表示为对角矩阵与低秩修正之和，实现高效的训练、推理和内存使用。我们推导出数值稳定的秩-1及批量更新方法，无需显式构造矩阵即可保持其逆。为控制内存增长，采用投影分裂积分器进行动态低秩逼近，使每步平均更新成本和内存使用量为O(dr)，其中r为逼近秩。所提算法每动作评估的推理复杂度为O(dr)。在推荐系统数据集上的实验验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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