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Distributed Network Processing and Optimization under Communication Constraint
thesisposted on 26.07.2021, 19:01 authored by Chang Shen LeeChang Shen Lee
In recent years, the amount of data in the information processing systems has significantly increased, which is also referred to as big-data. The design of systems handling big-data calls for a scalable approach, which brings distributed systems into the picture. In contrast to centralized systems, data are spread across the network of agents in the distributed system, and agents cooperatively complete tasks through local communications and local computations. However, the design and analysis of distributed systems, in which no central coordinators with complete information are present, are challenging tasks. In order to support communication among agents to enable multi-agent coordination among others, practical communication constraints should be taken into consideration in the design and analysis of such systems. The focus of this dissertation is to provide design and analysis of distributed network processing using finite-rate communications among agents. In particular, we address the following open questions: 1) can one design algorithms balancing a graph weight matrix using finite-rate and simplex communications among agents? 2) can one design algorithms computing the average of agents’ states using finite-rate and simplex communications? and 3) going beyond of ad-hoc algorithmic designs, can one design a black-box mechanism transforming a general class of algorithms with unquantized communication to their finite-bit quantized counterparts?
This dissertation addresses the above questions. First, we propose novel distributed algorithms solving the weight-balancing and average consensus problems using only finite-rate simplex communications among agents, compliant to the directed nature of the network topology. A novel convergence analysis is put forth, based on a new metric inspired by the
positional system representations. In the second half of this dissertation, distributed optimization subject to quantized communications is studied. Specifically, we consider a general class of linearly convergent distributed algorithms cast as fixed-point iterate, and propose a novel black-box quantization mechanism. In the proposed mechanism, a novel quantizer preserving linear convergence is proposed, which is proved to be more communication efficient than state-of-the-art quantization mechanisms. Extensive numerical results validate our theoretical findings.