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Adaptive social learning is a useful tool for studying distributeddecision-making problems over graphs. This paper investigates the effect ofcombination policies on the performance of adaptive social learning strategies.Using large-deviation analysis, it first derives a bound on the steady-stateerror probability and characterizes the optimal selection for the Perroneigenvectors of the combination policies. It subsequently studies the effect ofthe combination policy on the transient behavior of the learning strategy byestimating the adaptation time in the low signal-to-noise ratio regime. In theprocess, it is discovered that, interestingly, the influence of the combinationpolicy on the transient behavior is insignificant, and thus it is more criticalto employ policies that enhance the steady-state performance. The theoreticalconclusions are illustrated by means of computer simulations.

Optimal Aggregation Strategies for Social Learning over Graphs