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 monotonic 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方法使得解决这些问题的分布方法很受欢迎。与此同时,大多数分布式系统都有一个基本问题――沟通瓶颈。有多种方法可以解决这个问题。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,在解决分布顺利的、高度单调的差别性不平等方面,这种协同作用比每一种单独方法更有效。实验证实了理论结论。