这篇论文提出了去中心化网络下的卷积秩回归新框架，用ADMM高效求解，还给出了理论保证，做分布式学习的值得一看。
本文研究去中心化分布式学习网络中的卷积秩回归（CRR），提出一种新的去中心化CRR框架，通过核平滑秩损失与共识约束优化求解估计量。该方法仅依赖本地节点数据和邻居节点共享信息，实现隐私保护和高效通信。在异构网络设定下，论文为去中心化CRR估计量建立了有限样本误差界，并为稀疏去中心化CRR LASSO估计量推导了精确的支持恢复保证。通过广义共识ADMM求解局部子问题，数值模拟和真实数据实验验证了方法的优越性能。
Distributed Convolutional Rank Regression over Decentralized Networks
This paper studies convolution rank regression (CRR) over decentralized distributed learning networks. We propose a novel decentralized CRR framework, in which estimators are obtained by solving consensus-constrained optimization with kernel-smoothed rank loss. The developed estimation scheme relies solely on local node data and information shared by neighboring nodes, thereby achieving privacy preservation and high communication efficiency. For heterogeneous network settings, we establish finite-sample error bounds for the decentralized CRR estimator and derive exact support recovery guarantees for the sparse decentralized CRR LASSO estimator. To facilitate numerical implementation, we adopt a generalized consensus ADMM to efficiently solve local subproblems across all network nodes. We verify the favorable performance of our developed approach via extensive numerical simulations and real-data experiments.