Title:
Algorithmic, game theoretic and learning theoretic aspects of distributed optimization
Algorithmic, game theoretic and learning theoretic aspects of distributed optimization
Authors
Ehrlich, Steven Jeremy
Authors
Advisors
Balcan, Nina
Shamma, Jeff S.
Shamma, Jeff S.
Advisors
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Abstract
Distributed systems are fundamental to today's world. Many modern problems involve multiple agents either competing or coordinating across a network, and even tasks
that are not inherently distributed are often divided to accommodate today's computing resources. In this thesis we consider distributed optimization through the lens of several problems. We first consider the fragility of distributed systems, with an investigation in game
theory. The inefficiency, relative to total cooperation, of agents acting myopically in their own interest is well studied as the so called the Price of Anarchy. We assess how much
further the social welfare can degrade due to repeated small disruptions. We consider two
models of disruptions. In the first, agents perceive costs subject to a small adversarial perturbation; in the second a small number of Byzantine players attempt to influence the
system. For both models we improve upper and lower bounds on how much social welfare can degrade for several interesting classes of games. We next consider several problems in which agents have partial information and wish to efficiently coordinate on a solution. We measure the cost of their coordination by the amount of communication the agents must exchange. We next investigate a problem in active and semi-supervised learning. After providing a novel algorithm to learn it in the
centralized case, we consider the communication cost of this algorithm when the examples are
distributed amongst several agents. We then turn to the problem of clustering when the data
set has been distributed among many agents. Here we devise an algorithm for coordinating
on a global approximation that can be communicated efficiently by the use of coresets. Finally we consider a problem of submodular maximization where the objective function has been distributed among agents. We adapt a centralised approximation algorithm to the
distributed setting with efficient communication between the agents.
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Date Issued
2016-08-26
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Dissertation