论文标题
完全异步的大规模二次编程：正则化，收敛速率和参数选择
Totally Asynchronous Large-Scale Quadratic Programming: Regularization, Convergence Rates, and Parameter Selection
论文作者
论文摘要
二次程序在机器人技术，通信，智能电网和许多其他应用程序中出现。随着这些问题的增加，找到解决方案变得更加苛刻，需要新的算法来在大规模的尺度上有效地解决它们。针对大规模问题，我们开发了一个多代理二次编程框架，其中每个代理仅更新问题中的总决策变量的少数。代理商将其更新的值彼此传达，尽管我们对他们这样做的时机没有任何限制，也没有对这些传输的延迟施加任何限制。此外，我们允许代理之间的弱参数耦合，从某种意义上说，它们可以独立选择其步骤尺寸，受到轻度限制。我们进一步为代理人提供了独立规范它们解决的问题的手段，从而改善了收敛性能，同时保留了代理在选择参数时的独立性并确保满足正规化错误的全局限制。较大的正规化加速了收敛，但增加了获得的解决方案的误差，我们量化了收敛速率和解决方案质量之间的权衡。提出了仿真结果以说明这些发展。
Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes more computationally demanding, and new algorithms are needed to efficiently solve them at massive scales. Targeting large-scale problems, we develop a multi-agent quadratic programming framework in which each agent updates only a small number of the total decision variables in a problem. Agents communicate their updated values to each other, though we do not impose any restrictions on the timing with which they do so, nor on the delays in these transmissions. Furthermore, we allow weak parametric coupling among agents, in the sense that they are free to independently choose their step sizes, subject to mild restrictions. We further provide the means for agents to independently regularize the problems they solve, thereby improving convergence properties while preserving agents' independence in selecting parameters and ensuring a global bound on regularization error is satisfied. Larger regularizations accelerate convergence but increase error in the solution obtained, and we quantify the trade off between convergence rates and quality of solutions. Simulation results are presented to illustrate these developments.
