A control-theoretic approach to distributed optimization

优化自然出现在各种领域，例如管理无线频谱利用率，在电网中有效分配电力，或解决机器学习问题。这类应用的规模一直在稳步增长，通常迫使数据在通过通信网络连接的不同物理位置进行处理。随后的计算任务由分布式优化算法调解，这些算法精心编排了本地计算和与其他计算节点的全局同步的组合。这些分布式算法对于确保大型系统的安全性、可靠性、效率和性能至关重要。本项目旨在开发一种系统的方法来分析和设计这种分布式算法。该项目将分布式优化算法视为具有反馈的动态系统；在给定时间做出的决策会影响系统在未来时间的状态，从而影响未来的决策，依此类推。这种观点的优点是，它允许人们利用控制理论中的工具和方法，控制理论是一门建立良好的工程学科，用于设计现代安全关键系统，如飞机、汽车和工业工厂。将这些复杂的工具应用于分布式优化算法将使我们摆脱传统的增量设计方法，并具有高度变革的潜力。它将带来更好的分布式算法，但也会带来更有原则和自动化的设计方法，这些方法可以让算法直接合成并专门用于手头的任务。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Optimization arises naturally in a variety of areas, such as managing wireless spectrum utilization, efficiently distributing power in the electrical grid, or solving machine learning problems. The scale of such applications has been steadily growing, often forcing data to be processed in different physical locations linked via a communication network. The ensuing computational task is mediated by distributed optimization algorithms that carefully orchestrate a combination of local computations and global synchronization with the other computing nodes. These distributed algorithms are critical in ensuring the safety, reliability, efficiency, and performance of large-scale systems. This project aims to develop a systematic approach for analyzing and designing such distributed algorithms. This project will view distributed optimization algorithms as dynamical systems with feedback; decisions made at a given time affect the state of the system at future times, and therefore affect future decisions, and so on. The advantage of this viewpoint is that it allows one to leverage tools and methodology from control theory, which is a well established engineering discipline used in the design of modern safety-critical systems such as aircraft, automobiles, and industrial plants. Applying these sophisticated tools to distributed optimization algorithms will allow us to move away from conventional incremental design methods and has the potential to be highly transformative. It will lead to better distributed algorithms, but also more principled and automated design methods that can allow algorithms to be directly synthesized and specialized for the task at hand.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.