Clustering method cuts computing costs for linear bandits
Efficient Linear Bandits via Cluster-Aware Sketching
Machine Learning
Summary
In problems where a computer must choose options based on many features, calculations can become very slow as the number of features grows. The authors looked at a type of problem called linear bandits where this happens and designed a new approach using clustering. Their method groups similar data points and keeps detailed information within each group to avoid losing accuracy, while speeding up the calculations compared to earlier methods. Tests on made-up data show it balances being fast and making good decisions.
What this means in practice
- •For online advertising teams: Optimize ad selection efficiently when using many features describing users and ads without excessive computation.
- •For recommendation system engineers: Speed up decision updates in high-dimensional recommendation problems by clustering similar items to reduce computation costs.
Tested on simulated data.
Authors
Hantao Yang, Hong Xie, Defu Lian
Abstract
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.