On the Convergence of the Structural Estimation of Proximal Operator
with Gaussian Processes (STEP-GP) Method with Adaptive Quantization for
Communication-Efficient Distributed Optimization
Abstract
This technical note presents proof of the convergence of the Alternating
Direction Method of Multipliers (ADMM) for addressing the sharing
problem when applied in conjunction with two algorithms: 1) the
stochastic STEP-GP algorithm and 2) its variant named LGP, which
includes adaptive uniform quantization. For the case using LGP, the
coordinator can assign different quantization resolutions at each
iteration and we assume that the number of bits that can be assigned is
unrestricted and can go to infinity. This document describes and
analyzes the two methods for integrating learning and uniform
quantization into the ADMM to reduce its communication overhead and a
general formulation of their communication decision method. The problems
are formulated for a multi-agent setting.