There have been many recent works proposing new compressors for various distributed optimization settings. But, all cutting-edge performance analyses come down to one of the only two properties of compressors: unbiasedness or contraction. This leads to a natural question: If we want to improve the convergence rate of distributed optimization with communication compression, should we continue using those properties and focus on how to apply them more cleverly in distributed algorithms, or should we look for new compressor properties? To answer this question, we present theoretical performance lower bounds imposed by those two properties and, then, show that the lower bounds are nearly matched by a method, which works with any compressors satisfying one of those two properties. Hence, future work shall look for a fundamentally new compressor property.

This is joint work with Xinmeng Huang (UPenn), Yiming Chen (Alibaba), and Kun Yuan (Alibaba).