Reviews: LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning

This paper explores the question of minimizing the communication among workers while solving an optimization problem in a distributed fashion. In particular, the authors argue that most of the existing work in this direction focused on minimizing the amount of data during each message exchange between the works. In contrast, the authors focus on reducing the number of such exchanges (or communication rounds) during the optimization procedures. The authors argue that reducing the number of rounds is more beneficial as it does not degrade the rate of convergence for a wide class of objective functions. The authors propose a simple approach to reduce the communication: a worker sends the current values of the gradient (based on its data) only if this gradient is significantly far from the previous gradient supplied by this worker, leading to the name lazily aggregated gradient (LAG).