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Online Learning of Dynamic Parameters in Social Networks
This paper addresses the problem of online learning in a dynamic setting. We
consider a social network in which each individual observes a private signal
about the underlying state of the world and communicates with her neighbors at
each time period. Unlike many existing approaches, the underlying state is
dynamic, and evolves according to a geometric random walk. We view the scenario
as an optimization problem where agents aim to learn the true state while
suffering the smallest possible loss. Based on the decomposition of the global
loss function, we introduce two update mechanisms, each of which generates an
estimate of the true state. We establish a tight bound on the rate of change of
the underlying state, under which individuals can track the parameter with a
bounded variance. Then, we characterize explicit expressions for the steady
state mean-square deviation(MSD) of the estimates from the truth, per
individual. We observe that only one of the estimators recovers the optimal
MSD, which underscores the impact of the objective function decomposition on
the learning quality. Finally, we provide an upper bound on the regret of the
proposed methods, measured as an average of errors in estimating the parameter
in a finite time.Comment: 12 pages, To appear in Neural Information Processing Systems (NIPS)
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