  Edge networks call for communication efficient (low overhead) and robust
distributed optimization (DO) algorithms. These are, in fact, desirable
qualities for DO frameworks, such as federated edge learning techniques, in the
presence of data and system heterogeneity, and in scenarios where internode
communication is the main bottleneck. Although computationally demanding,
Newton-type (NT) methods have been recently advocated as enablers of robust
convergence rates in challenging DO problems where edge devices have sufficient
computational power. Along these lines, in this work we propose Q-SHED, an
original NT algorithm for DO featuring a novel bit-allocation scheme based on
incremental Hessian eigenvectors quantization. The proposed technique is
integrated with the recent SHED algorithm, from which it inherits appealing
features like the small number of required Hessian computations, while being
bandwidth-versatile at a bit-resolution level. Our empirical evaluation against
competing approaches shows that Q-SHED can reduce by up to 60% the number of
communication rounds required for convergence.
