Decentralized Byzantine‐Resilient Primal–Dual Fixed Point Algorithm for Blockwise Low‐Rank Matrix Learning

ABSTRACT In this paper, we propose a decentralized Byzantine‐resilient primal–dual fixed point (BR‐PDFP) algorithm, a robust solution for blockwise low‐rank matrix learning in decentralized settings. The BR‐PDFP algorithm is specifically designed to be efficient and resilient against Byzantine failures, guaranteeing reliable performance in decentralized optimization even in the face of attacks. Applying resilient consensus steps with the proximal operator over a network, our algorithm is optimized for decentralized systems. It has been proven to be highly effective in the domain of image recovery. Comprehensive theoretical analyses of the computational and communication complexities of the algorithm are provided. Moreover, we show that our algorithm enjoys global linear convergence under strong convexity. With blockwise regularization, we empirically validate the performance of the algorithm, highlighting its scalability, resilience and recovery capabilities.