The distributed optimization problem has become increasingly relevant recently. It has a lot of advantages such as processing a large amount of data in less time compared to non-distributed methods. However, most distributed approaches suffer from a significant bottleneck - the cost of communications. Therefore, a large amount of research has recently been directed at solving this problem. One such approach uses local data similarity. In particular, there exists an algorithm provably optimally exploiting the similarity property. But this result, as well as results from other works solve the communication bottleneck by focusing only on the fact that communication is significantly more expensive than local computing and does not take into account the various capacities of network devices and the different relationship between communication time and local computing expenses. We consider this setup and the objective of this study is to achieve an optimal ratio of distributed data between the server and local machines for any costs of communications and local computations. The running times of the network are compared between uniform and optimal distributions. The superior theoretical performance of our solutions is experimentally validated.
Nanjing Normal University（南京师范大学）；Key Laboratory of NSLSCS (NNU), Ministry of Education, P.R. China（教育部非线性和系统科学重点实验室（南师大））；Nanjing University of Science and Technology（南京理工大学）
Variable Stepsize Distributed Forward-Backward Splitting Methods as Relocated Fixed-Point Iterations
Centro de Modelamiento Matemático (CNRS IRL2807), Universidad de Chile（智利大学数学建模中心）；School of Science, RMIT University（皇家墨尔本理工大学理学院）；School of Mathematics & Statistics, The University of Melbourne（墨尔本大学数学与统计学院）
Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control
Department of Applied Mathematics, The Hong Kong Polytechnic University（应用数学系，香港理工大学）；College of Artificial Intelligence, Nankai University（人工智能学院，南开大学）
A distributed primal-dual algorithm for computation of generalized Nash equilibria with shared affine coupling constraints via operator splitting methods
Graph and distributed extensions of the Douglas-Rachford method
在本文中，我们提出了几个基于图的道格拉斯-Rachford分裂（DRS）方法解决单调包含问题涉及$N$极大单调算子的总和。我们的建设是基于一个两层的架构，我们称之为二层图，我们相关联的DRS算法，提出了规定的结构的泛化。所得到的方案可以被理解为在Ryu [Math Program 182（1）：233-273，2020]的意义上具有最小提升的无条件稳定的节俭预解式分裂方法，以及（退化）预处理邻近点方法的实例，其提供了鲁棒的收敛保证。我们进一步描述了如何利用DRS方法的基于图的扩展来设计新的完全分布式协议。一个拥挤的最优输运问题和分布式支持向量机的应用程序显示出有趣的连接与底层图形拓扑结构和高度竞争的性能与国家的最先进的分布式优化方法。
Operator Splitting, Policy Iteration, and Machine Learning for Stochastic Optimal Control
The University of Texas at Dallas（德克萨斯大学达拉斯分校）；International University - Vietnam National University HCM City（越南国立大学胡志明市国际大学）；Texas A&M University（德克萨斯农工大学）；Baylor University（贝勒大学）
Alternating Direction Method of Multipliers for nonlinear constrained convex problems and applications to distributed resource allocation and constrained machine learning
