发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维线性老虎机计算成本高的问题，提出基于聚类感知草图化的CS-LB算法，通过保留聚类协方差信息实现亚线性遗憾，并将每轮计算降至O(l^2d)。
AI 中文摘要
我们研究了在有限臂集的高维设置下线性老虎机的计算效率问题。在线性老虎机中，特征向量维度$d$的增加导致每轮更新的计算成本以$O(d^2)$增长。传统的基于草图化的方法（如SOFUL）通过固定大小的矩阵草图化来降低计算成本，但当数据的谱尾较重且草图大小选择不当时，这些方法可能产生无意义的线性遗憾。为了保证遗憾收敛并有效降低计算成本，我们引入了一种聚类机制，并提出了聚类草图线性老虎机（CS-LB）算法。我们的方法在每个聚类中保留完整的协方差信息，以确保在没有谱尾脆弱性的情况下实现稳健的亚线性遗憾；通过为每个聚类分配一个哨兵来执行聚类切换，并通过可调的草图大小$l<d$将每轮更新计算降低到$O(l^2d)$。在合成数据集上的实验表明，我们的方法始终能在效率和遗憾之间保持有利的权衡。
英文摘要
We study the problem of computational efficiency for linear bandits in high-dimensional settings with a finite arm set. In linear bandits, the increase in the dimension $d$ of the feature vectors leads to growing computational costs of $O(d^2)$ at each round of update. Traditional sketching-based methods such as SOFUL reduce computation via fixed-size matrix sketching, yet run the risk of incurring vacuous linear regret when the spectral tail of the data is heavy and the sketch size is inadequately selected. To guarantee regret convergence and effectively reduce computational costs, we introduce a clustering mechanism and propose the Cluster Sketch Linear Bandit (CS-LB) algorithm. Our method preserves the full covariance information in each cluster to guarantee robust sublinear regret without spectral-tail vulnerabilities, performs cluster switching by assigning a sentinel for each cluster, and reduces per-round update computation to $O(l^2d)$ via a tunable sketch size $l<d$. Experiments on synthetic datasets demonstrate that our method consistently maintains a favorable trade-off between efficiency and regret.
