Linearly Convergent Distributed Optimization Methods with Compressed Innovation
Jiaqi Zhang, Keyou You · 2021 60th IEEE Conference on Decision and Control (CDC) · 2021
Data compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. In this work, we propose a novel communication-efficient linearly convergent distributed (COLD) algorithm with compressed innovation—the difference between a model and its estimate. COLD supports a class of quantizers with δ-contraction property. For strongly convex distributed problems, we explicitly quantify in theory how the compression affects the linear convergence rate. To the best of our knowledge, we are the first to achieve linear convergence in distributed optimization allowing biased and δ-contracted compressors, which is a typical case in practice. Numerical experiments validate our theoretical results.