A control-theoretic approach to distributed optimization

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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.