Efficient Information Aggregation Strategies for Distributed Control and Signal Processing

TL;DR

This thesis develops efficient decentralized algorithms for averaging and function computation in large-scale, dynamic networks, enabling robust distributed control and signal processing.

Contribution

It introduces the fastest averaging algorithms under various constraints, establishes fundamental lower bounds, and proposes a new model for distributed function computation.

Findings

Derived the fastest known averaging algorithms for different settings.

Proved a lower bound indicating a fundamental limit for averaging algorithms.

Nearly characterized the class of functions computable in the new distributed model.

Abstract

This thesis is concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model.