Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributed online second-order dynamics for convex optimization over switching connected graphs
D. Mateos -Nuñez, J. Cortés
International Symposium on Mathematical Theory of Networks
and Systems, Groningen, The Netherlands, 2014, pp. 15-22
Abstract
This paper studies the regret of a family of distributed algorithms
for online convex unconstrained optimization. A team of agents
cooperate in a decision making process enabled by local
interactions and the knowledge of each agent about the local cost
functions associated with its decisions in previous rounds. We
propose a class of online, second-order distributed coordination
algorithms that combine subgradient descent on the local objectives
revealed in the previous round and proportional-integral feedback
on the disagreement among neighboring agents. The communication
network is given by a time-varying sequence of connected graphs,
and the local objectives can be adversarially adaptive to the
agents' behavior. The goal of each agent is to incur a cumulative
cost over time with respect to the sum of local objectives across
the network that is competitive with the best fixed and centralized
decision in hindsight. For this, we establish the classical
logarithmic regret bound under strong convexity of the local
objectives.
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Mechanical and Aerospace Engineering,
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