基于网络的近端多任务学习与稀疏共正则化
Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization
AI总结：
本文提出一种分布式算法，通过非可微项促进邻域集群合作，利用加权ℓ1范数的闭式表达式提升效率，并通过仿真实验验证了方法的有效性。
摘要：
在本文中，我们考虑了多任务学习问题，其中节点集群希望估计自身的参数向量。当相邻集群的最优模型具有大量相似元素时，集群间的合作是有益的。我们提出了一种完全分布式算法来解决此问题。该方法依赖于最小化一个全局均方误差准则，通过非可微项进行正则化以促进邻域集群之间的合作。引入了一种通用的扩散前向-后向分裂策略，然后将其专门应用于促进稀疏性的正则化。推导了加权ℓ1范数之和的近 operator 的闭式表达式以实现更高的效率。我们还提供了步长条件，以确保算法在均值和均方误差意义下的收敛性。通过仿真验证了该策略的有效性。
英文摘要：
In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of $\ell_1$-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
