Adaptive Social Learning

Abstract

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

Network Classifiers Based on Social Learning

“…However, agents might not have enough information to solve this classification problem alone, e.g., if the signals at agent k are not informative enough (for example, it may be the case that L k (h| − 1) = L k (h| + 1) for all h ∈ H k ). If however the network as a whole possesses enough information, under the weaker assumption of global identifiability, then a social learning scheme can be used and allows agents to learn the truth [1,4,5,7,8].…”

“…The log-likelihood ratio on the RHS of ( 3) is positive whenever the observation h k,i is more likely to have come from class +1 and negative when it is more likely to have originated from class −1. This is the same sufficient statistic aggregated over space and time in social learning [7,14] and in signal detection schemes [13,16,17].…”

“…which is computed over the training set. Since agents solve (7) until convergence, we assume they reach an empirical minimizer f N k that is close enough to the target f o k for sufficiently large N k under ergodicity assumptions. Next, we introduce the algorithm that allows these classifiers to be combined within a network.…”

“…Social learning strategies allow the classification of unlabeled features by a heterogeneous network of agents [1][2][3][4][5][6][7][8]. The heterogeneity of the network is twofold: first, agents may be observing different (possibly non-overlapping) sets of attributes of the same underlying phenomenon; second, their statistical models need not be the same, e.g., two agents may be observing the same attribute from different perspectives.…”

“…We therefore propose the Social Machine Learning (SML) approach: a decentralized algorithm for combining the outputs of a heterogeneous network of classifiers over space and time, based on the adaptive diffusion algorithm proposed in [7,13,14]. The SML structure inherits the following qualities from social learning: the ability to combine classifiers with different dimensions and statistical models, while providing asymptotic performance guarantees in addition to continuous performance improvement even during the prediction phase.…”