Cooperative Thresholded Lasso for Sparse Linear Bandit

TL;DR

This paper introduces a multi-agent sparse linear bandit algorithm that uses Lasso for feature selection, reduces communication costs, and achieves near-optimal regret bounds in high-dimensional settings.

Contribution

It proposes the first distributed algorithm for sparse linear bandits with row-wise data sharing, combining Lasso and ridge regression for efficient multi-agent learning.

Findings

Achieves regret bound of order O(s_0 log d + s_0 √T) with high probability.

Reduces communication costs while maintaining near-optimal regret performance.

Demonstrates effectiveness on synthetic and real-world datasets.

Abstract

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 $s_0 \ll d$. 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 $\mathcal{O}(s_0 \log d + s_0 \sqrt{T})$ 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.