We have just posted a preprint titled: “A Canonical Form for First-Order Distributed Optimization Algorithms”. It is available here and on arXiv. This is joint work with my student Akhil Sundararajan, my postdoc Bryan Van Scoy, and myself. Our work provides a canonical form for distributed optimization algorithms that will enable more streamlined analysis and design.

There has been much recent interest in the analysis and design of distributed optimization algorithms. In this context, “distributed” means that the computation happens on different computers across a network. Each computing node may have access to different local information. The goal is for each node to arrive at the solution of a global optimization problem that involves everybody’s data, whilst each node only performs local computation and communicates only with nearby nodes. All of this should happen without ever needing to store all the data in one place. This paradigm makes sense in cases where the individual nodes are remote and have limited computing capability, or we are trying to conserve power by transmitting and computing as little as possible. Also, we may not want a single node to gather and store all the available information for privacy or security reasons.

In the past 5 years, other researchers have proposed a variety of solutions to this problem. Proposed methods involve local computation, local memory updates, and communication with nearby nodes, in some prescribed order. Because there is a number of different ways to perform these actions, there is a combinatorial explosion of possible designs, analyses, and outcomes.

Our paper provides a way of streamlining research efforts in this area: we showed that in fact, there aren’t that many different possible distributed optimization algorithms. We were able to parameterize a broad sub-family of algorithms using only 5 scalar parameters. In doing so, we were able to neatly categorize existing methods and in some cases, show that different established algorithms were in fact the same algorithm!

Our hope is that this work will help streamline research efforts in distributed optimization in moving toward a more principled understanding of analysis and design.