Social Learning and Distributed Hypothesis Testing

ISIT Student Paper Award). This paper considers the problem of distributed hypothesis testing and social learning. Suppose individual nodes in a network receive noisy (private) obser-vations whose distribution is parameterized by one of M parameters (hypotheses). The distributions are known locally at the nodes, but the true parameter/hypothesis is not known. If the local observations are insufficient to recover the underlying parameter (for example, low dimensional measurements of a higher-dimensional parameter), individuals must share and learn from each other in order to accurately infer the true parameter. Inspired by recent non-Bayesian social learning algorithms, the updating of opinions of each node is broken down into two steps: a local-Bayesian update, which incorporates the noisy observations and the known parametric distribution of the noise, and a new non-Bayesian update rule which merges the nodes ’ opinions. It is shown that each node’s opinion/belief about any hypothesis whose truth is inconsistent with the overall network-wide observations vanishes to zero exponentially fast. In other words, each node’s opinion converges to the true underlying parameter exponentially fast. This new method of merging opinions allows for a concise proof of the convergence and a closed form characterization of rate of convergence. Furthermore, the exponential rate of learning is shown to be both a function of the nodes ’ collective ability to discriminate among the hypotheses set as well as the social structure of the network. I