# Efficient Linear Bandits via Cluster-Aware Sketching

arXiv: https://arxiv.org/abs/2609.27594 · HTML: https://mlsanity.com/paper/2609.27594/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [Frequent Directions : Simple and Deterministic Matrix Sketching](https://mlsanity.com/paper/1501.01711/) (2015)
- [Subspace Embedding and Linear Regression with Orlicz Norm](https://mlsanity.com/paper/1806.06430/) (2018)
- [Efficient Linear Bandits through Matrix Sketching](https://mlsanity.com/paper/1809.11033/) (2018)
- [Revisiting Matrix Sketching in Linear Bandits: Achieving Sublinear Regret via Dyadic Block Sketching](https://mlsanity.com/paper/2410.10258/) (2024)
- [Beyond Johnson-Lindenstrauss: Uniform Bounds for Sketched Bilinear Forms](https://mlsanity.com/paper/2509.21847/) (2025)

## Abstract (arXiv)

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(d2) 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(l2d) 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.