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.

翻译：我们提出了一种新颖的方法来解决多智能体稀疏上下文线性赌博机问题，其中特征向量具有高维度$d$，而奖励函数仅依赖于有限的特征集——确切地说为$s_0 \ll d$。此外，学习过程遵循信息共享约束。该方法采用Lasso回归进行降维，使每个智能体能够独立估计一组主要维度的近似集，并根据网络结构将该信息与其他智能体共享。信息通过特定流程聚合后分发给所有智能体。随后，每个智能体仅针对提取的维度使用岭回归解决问题。我们分别针对星形网络和点对点网络设计了算法。这些方法在确保每个智能体累积遗憾最小的同时，有效降低了通信成本。理论上，我们证明了所提方法以高概率具有$\mathcal{O}(s_0 \log d + s_0 \sqrt{T})$的遗憾界，其中$T$为时间范围。据我们所知，这是首个解决稀疏线性赌博机中行式分布式数据的算法，其性能与最先进的单智能体和多智能体方法相当。此外，该方法广泛适用于高维多智能体问题，其中高效的特征提取对于最小化遗憾至关重要。为验证方法的有效性，我们展示了在合成数据集和真实数据集上的实验结果。