Compression and Data Similarity: Combination of Two Techniques for Communication-Efficient Solving of Distributed Variational Inequalities

Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems popular. Meanwhile, most distributed systems have a basic problem - a communication bottleneck. There are various techniques to deal with it. In particular, in this paper we consider a combination of two popular approaches: compression and data similarity. We show that this synergy can be more effective than each of the approaches separately in solving distributed smooth strongly monotone variational inequalities. Experiments confirm the theoretical conclusions.