Decentralized Byzantine‐Resilient Dictionary Learning

Decentralized dictionary learning has been a hot topic in recent years. However, there is a scarcity of research related to scenarios involving Byzantine attacks. In this paper, we introduce a novel decentralized Byzantine‐Resilient Dictionary Learning (BRDL) algorithm, designed to address the dual challenges of data distribution across decentralized networks and potential Byzantine failures. By leveraging techniques such as alternating optimization, decentralized gradient descent and coordinate‐wise trimmed‐mean (CTM), the algorithm ensures both convergence and resilience against Byzantine attacks. Theoretical analysis demonstrates that the algorithm achieves consensus among honest nodes and guarantees the convergence of the objective function even in the presence of latent Byzantine attacks. Simulations and real‐world applications validate the effectiveness of our algorithm in handling Byzantine attacks, demonstrating its superior robustness compared with mainstream decentralized dictionary learning methods.