Innovation Compression for Communication-Efficient Distributed Optimization With Linear Convergence

Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This article proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly convex optimization problems. By compressing innovation vectors, which are the differences between decision vectors and their estimates, COLD achieves linear convergence for a class of
$\delta$
-contracted compressors, and we explicitly quantify how the compression affects the convergence rate. Interestingly, our results strictly improve existing results for the quantized consensus problem. Numerical experiments demonstrate the advantages of COLD under different compressors.