Non-Bayesian Social Learning with Uncertain Models
This addresses a limitation in distributed inference for networked agents by handling model uncertainty, but it is incremental as it extends existing social learning frameworks.
The paper tackles the problem of non-Bayesian social learning when agents have uncertain statistical models learned from finite data, proposing a rule that incorporates second-order probabilities to make beliefs sensitive to prior evidence, and shows that learning converges to traditional theory as evidence increases.
Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown state of the world with their neighbors using a learning rule. Existing approaches assume agents have access to precise statistical models (in the form of likelihoods) for the state of the world. However in many situations, such models must be learned from finite data. We propose a social learning rule that takes into account uncertainty in the statistical models using second-order probabilities. Therefore, beliefs derived from uncertain models are sensitive to the amount of past evidence collected for each hypothesis. We characterize how well the hypotheses can be tested on a social network, as consistent or not with the state of the world. We explicitly show the dependency of the generated beliefs with respect to the amount of prior evidence. Moreover, as the amount of prior evidence goes to infinity, learning occurs and is consistent with traditional social learning theory.