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.

翻译：差异性不平等是一个重要的工具,包括最小化、马鞍、游戏、固定点问题。现代大规模和计算成本昂贵的实用应用使分配解决这些问题的方法广为人知。与此同时,大多数分布式系统都有一个基本问题,即沟通瓶颈。有各种应对方法。特别是,在本文件中,我们考虑两种流行方法的结合:压缩和数据相似性。我们表明,这种协同效应在解决分布顺利的、明显的单调差异性不平等方面比每一种方法更为有效。实验证实了理论结论。