Collecting the most informative data from a large dataset distributed over a network is a fundamental problem in many fields, including control, signal processing and machine learning. In this paper, we establish a connection between selecting the most informative data and finding the top-$k$ elements of a multiset. The top-$k$ selection in a network can be formulated as a distributed nonsmooth convex optimization problem known as quantile estimation. Unfortunately, the lack of smoothness in the local objective functions leads to extremely slow convergence and poor scalability with respect to the network size. To overcome the deficiency, we propose an accelerated method that employs smoothing techniques. Leveraging the piecewise linearity of the local objective functions in quantile estimation, we characterize the iteration complexity required to achieve top-$k$ selection, a challenging task due to the lack of strong convexity. Several numerical results are provided to validate the effectiveness of the algorithm and the correctness of the theory.

通过使用平滑技术，本文提出了一种加速方法，旨在解决网络规模的局部目标函数缺乏光滑性时导致的收敛速度慢和可扩展性差的问题，以实现具有分布式凸优化的多元集合下的前k个元素选择。

通过分布式平滑分位数估计进行快速网络数据选择