Distributed Optimization Beyond Worst-Case Topologies

ended

Modern systems are increasingly dezentralized and massively distributed computations play a vital role in the systems of the future. This project aims to advance the foundational aspects of distributed computing, particularly MessagePassing algorithms for optimization problems. The strong shift towards distributed systems also lead to a flurry of works on such algorithms -- many optimization problems now have distributed algorithms with optimal worst-case performance guarantees. Generally, these guarantees cannot be improved because they match unconditional impossibility results, which prove severe limitations on the performance of distributed algorithms in some (pathological) network topologies. Real world networks, however, are never worst-case and do not share the limiting bottleneck characteristics of these pathological topologies. In fact, there is no known barrier for ultra-fast polylogarithmic-round distributed algorithms on any network of interest. This leaves an exponential gap between current worst-case-optimal algorithms and what is likely possible in many, if not all, real-world settings. Motivated by this, this project provides a program for a general toolbox and theory for MessagePassing optimization algorithms that go beyond worst-case topologies. The main and guiding high-risk high-gain goal is the development of universally optimal distributed algorithms, which are competitive with the best algorithm on any given topology. This would constitute the strongest possible form of algorithmically adjusting to non-worst-case topologies. A detailed program with many concrete and smaller stepping stones towards this ambitious breakthrough objective is provided. Many of the novel questions stemming from this program and proposal are highly interdisciplinary, crossing boundaries between information theory, distributed computing, topological graph theory, and other parts of theoretical computer science, and are fundamental and interesting in their own right.