Adaptive Social Learning

This work proposes a novel strategy for social learning by introducing the critical feature of adaptation. In learning, several distributed agents update continually their belief about phenomenon interest through: i) direct observation streaming data that they gather locally; and ii) diffusion beliefs through local cooperation with neighbors. Traditional implementations are known to learn well underlying hypothesis (which means every individual agent peaks at true hypothesis), achieving steady improvement in accuracy under stationary conditions. However, these algorithms do not perform nonstationary conditions commonly encountered online exhibiting significant inertia track drifts data. order address this gap, we propose an Adaptive Social Learning (ASL) strategy, which relies on small step-size parameter tune adaptation degree. First, provide detailed characterization performance steady-state analysis. Focusing regime, establish ASL achieves consistent standard global identifiability assumptions. We derive reliable Gaussian approximations probability error (i.e., choosing wrong hypothesis) each agent. carry out large deviations analysis revealing universal behavior adaptive learning: probabilities decrease exponentially fast inverse step-size, characterize resulting exponential rate. Second, transient analysis, allows us obtain useful analytical formulas relating time step-size. The revealed dependence highlights fundamental trade-off between emerging learning.