# Cooperative Thresholded Lasso for Sparse Linear Bandit

arXiv: https://arxiv.org/abs/2305.19161 · HTML: https://mlsanity.com/paper/2305.19161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Differentially-Private Federated Linear Bandits](https://mlsanity.com/paper/2010.11425/) (2020)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Distributed Clustering of Linear Bandits in Peer to Peer Networks](https://mlsanity.com/paper/1604.07706/) (2016)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [Improved Algorithm on Online Clustering of Bandits](https://mlsanity.com/paper/1902.09162/) (2019)
- [The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits](https://mlsanity.com/paper/2001.05452/) (2020)
- [Cooperative Multi-Agent Bandits with Heavy Tails](https://mlsanity.com/paper/2008.06244/) (2020)
- [Kernel Methods for Cooperative Multi-Agent Contextual Bandits](https://mlsanity.com/paper/2008.06220/) (2020)
- [Robust Multi-Agent Multi-Armed Bandits](https://mlsanity.com/paper/2007.03812/) (2020)
- [Multi-armed Bandits with Application to 5G Small Cells](https://mlsanity.com/paper/1510.00627/) (2015)
- [Thresholded Lasso Bandit](https://mlsanity.com/paper/2010.11994/) (2020)
- [Multi-Agent Low-Dimensional Linear Bandits](https://mlsanity.com/paper/2007.01442/) (2020)
- [A GPS spoofing detection and classification correlator-based technique using the LASSO](https://mlsanity.com/paper/2004.13900/) (2020)
- [Decentralized Multi-Agent Linear Bandits with Safety Constraints](https://mlsanity.com/paper/2012.00314/) (2020)
- [Adaptive Clustering and Personalization in Multi-Agent Stochastic Linear Bandits](https://mlsanity.com/paper/2106.08902/) (2021)
- [DecVi: Adaptive Video Conferencing on Open Peer-to-Peer Networks](https://mlsanity.com/paper/2209.00695/) (2022)

## Abstract (arXiv)

We present a novel approach to address the multi-agent sparse contextual linear bandit problem, in which the feature vectors have a high dimension d whereas the reward function depends on only a limited set of features - precisely s0 ll d. Furthermore, the learning follows under information-sharing constraints. The proposed method employs Lasso regression for dimension reduction, allowing each agent to independently estimate an approximate set of main dimensions and share that information with others depending on the network's structure. The information is then aggregated through a specific process and shared with all agents. Each agent then resolves the problem with ridge regression focusing solely on the extracted dimensions. We represent algorithms for both a star-shaped network and a peer-to-peer network. The approaches effectively reduce communication costs while ensuring minimal cumulative regret per agent. Theoretically, we show that our proposed methods have a regret bound of order O(s0 log d + s0 √T) with high probability, where T is the time horizon. To our best knowledge, it is the first algorithm that tackles row-wise distributed data in sparse linear bandits, achieving comparable performance compared to the state-of-the-art single and multi-agent methods. Besides, it is widely applicable to high-dimensional multi-agent problems where efficient feature extraction is critical for minimizing regret. To validate the effectiveness of our approach, we present experimental results on both synthetic and real-world datasets.