Quantized consensus ADMM for multi-agent distributed optimization

Abstract

This paper considers multi-agent distributed optimization with quantized communication which is needed when inter-agent communications are subject to finite capacity and other practical constraints. To minimize the global objective formed by a sum of local convex functions, we develop a quantized distributed algorithm based on the alternating direction method of multipliers (ADMM). Under certain convexity assumptions, it is shown that the proposed algorithm converges to a consensus within log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1+η</sub> Ω iterations, where η > 0 depends on the network topology and the local objectives, and O is a polynomial fraction depending on the quantization resolution, the distance between initial and optimal variable values, the local objectives, and the network topology. We also obtain a tight upper bound on the consensus error which does not depend on the size of the network.