Accelerated Distributed Directed Optimization With Time Delays

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Sähkötekniikan korkeakoulu | Master's thesis
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Date

2021-06-14

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Major/Subject

Control, Robotics and Autonomous Systems

Mcode

ELEC3025

Degree programme

AEE - Master’s Programme in Automation and Electrical Engineering (TS2013)

Language

en

Pages

51

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Abstract

With the rise of various constraints in centralized frameworks, decentralized computing and optimization have received major attention from the control community in recent times. In distributed optimization, chunks of the global objective are distributed over a set of agents that can communicate over a network. Each agent contributes by minimizing its local private objective and the global optimizer is a sum of local objective functions at each agent. Distributed systems that we focus on are represented by strongly connected directed graphs. For such a class of problems, Accelerated Distributed Directed Optimization (ADD-OPT) is a popular distributed optimization technique that is best known for faster linear convergence with wider and realistic step-sizes in contrast to existing work related to digraphs with column-stochastic weights. However, ADD-OPT is applicable only in a scenario where all agents communicate synchronously. Since agents are coordinating over a network, communication is a vital part of such systems. Propagation delays are the most common problem in any communication channel. The salient feature of this thesis is to study the robustness of ADD-OPT in presence of arbitrary and bounded propagation delays. The proposed algorithm is applicable in directed delay graphs based on existing ADD-OPT. The delay links introduce transients in the system but do not affect the convergence slope or rate. Further, higher delays shrink the range of step sizes, and for step-sizes near the upper bound, even smaller delays destabilize the system.

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Supervisor

Charalambous, Themistoklis

Thesis advisor

Charalambous, Themistoklis

Keywords

distributed optimization, directed graphs, time delays, distributed systems, linear convergence, step-size

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https://urn.fi/URN:NBN:fi:aalto-202106207536

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[dipl] Sähkötekniikan korkeakoulu / ELEC