In social learning, a network of agents assigns probability scores (beliefs)
to some hypotheses of interest, which rule the generation of local streaming
data observed by each agent. Belief formation takes place by means of an
iterative two-step procedure where: io) the agents update locally their beliefs
by using some likelihood model; and ii) the updated beliefs are combined with
the beliefs of the neighboring agents, using a pooling rule. This procedure can
fail to perform well in the presence of dynamic drifts, leading the agents to
incorrect decision making. Qui, we focus on the fully online setting where
both the true hypothesis and the likelihood models can change over time. Noi
propose the doubly adaptive social learning ($\text{A}^2\text{SL}$) strategy,
which infuses social learning with the necessary adaptation capabilities. Questo
goal is achieved by exploiting two adaptation stages: io) a stochastic gradient
descent update to learn and track the drifts in the decision model; ii) and an
adaptive belief update to track the true hypothesis changing over time. Questi
stages are controlled by two adaptation parameters that govern the evolution of
the error probability for each agent. We show that all agents learn
consistently for sufficiently small adaptation parameters, in the sense that
they ultimately place all their belief mass on the true hypothesis. In
particular, the probability of choosing the wrong hypothesis converges to
values on the order of the adaptation parameters. The theoretical analysis is
illustrated both on synthetic data and by applying the $\text{A}^2\text{SL}$
strategy to a social learning problem in the online setting using real data.

Questo articolo esplora i giri e le loro implicazioni.

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