摘要
This paper studies the distributed optimization problem over an undirected connected graph subject to digital communications with a finite data rate,where each agent holds a strongly convex and smooth cost function.The agents need to cooperatively minimize the average of all agents’cost functions.Each agent builds an encoder/decoder pair that produces transmitted messages to its neighbors with a finite-level uniform quantizer,and recovers its neighbors’states by a recursive decoder with received quantized signals.Combining the adaptive encoder/decoder scheme with the gradient tracking method,the authors propose a distributed quantized algorithm.The authors prove that the optimization can be achieved at a linear rate,even when agents communicate at 1-bit data rate.Numerical examples are also conducted to illustrate theoretical results.
