Sparse Optimization Algorithm for Robust Learning in Multi-Agent Systems

This paper proposes a sparse optimization algorithm for robust learning in Multi-Agent Systems (MAS) based on the alternating direction method of multipliers (ADMM) named Huber-DRLSP by reasonably defining the global loss function. The algorithm focuses on solving machine learning (ML) problems of distributed data or large-scale data that contain noisy data. Furthermore, by incorporating a sparse penalty term, the algorithm gains feature selection capabilities, improving its generalization performance. The theoretical analysis provides an explicit relationship between utility and penalty parameters, along with a linear convergence rate of $O(1/K)$, where $K$ represents the number of iterations. The simulation results verify the theoretical findings and demonstrate the robustness and effectiveness of the algorithm.