I attended the 23rd International Symposium on Mathematical Programming in Bordeaux, France. ISMP is an optimization conference that is held once every three years and it was my first time ever attending. It was also my first time visiting the south of France since my childhood. A nice opportunity to enjoy French cooking and do a bit of sightseeing… On the right is the Église Sainte-Croix de Bordeaux, a Roman Catholic church that dates back to the 11th century.
At the conference, I gave a 30-min talk on our recent work in distributed optimization. Distributed optimization has been a popular recent topic in the field of controls. The basic setup is that a distributed network of agents are trying to jointly optimize a cost function while only having access to a subset of the globally available data. For example, you can imagine a network of robots equipped with sensors, each of which can gather local information, perform computations, and share data with its neighbors. The goal is to have all agents eventually converge on a global model that accounts for all available data. Performing the computation in a decentralized fashion results in a system that is robust to changes such as an agent malfunctioning or communication links randomly failing.
Specifically, we used a robust control framework to analyze and compare the performance of various distributed optimization algorithms. While pure iterative optimization algorithms (with no distributed component) and pure consensus algorithms (information sharing but no optimization) have been extensively analyzed, the theory behind distributed optimization (a combination of optimization and consensus) is not as mature. Our hope is that the sorts of automated tools we are developing will help further our understanding of distributed algorithms, in the sense of analysis as well as design. This was joint work with my student Akhil Sundararajan and my postdocs Bryan Van Scoy and Bin Hu. The slides for my talk are available here.
My postdoc Bryan Van Scoy also came to ISMP and gave a talk of his own on an accelerated optimization algorithm he developed called the Triple Momentum Method. It is the fastest known accelerated method in the sense that it has the best worst-case performance over the set of strongly convex functions. For more information and for a link to slides, check out Bryan’s website!