# Correlated Data

The work introduces cordial (correlated and distributed) learning for distributed learning tasks where agents' data are correlated: an agent's label depends on other agents' inputs for the same sample, and those inputs are themselves correlated; the method shares only low-dimensional outputs between agents while training local models to extract informative signals from peers, inducing a game in which each agent's loss depends on others' models, and the authors prove convergence with probability one to a globally optimal solution under a linear model despite the nonconvex global objective, with experiments on structured multi-digit MNIST tasks showing the method remains highly effective even in highly nonlinear settings.

The work introduces cordial (correlated and distributed) learning for distributed learning tasks where agents' data are correlated: an agent's label depends on other agents' inputs for the same sample, and those inputs are themselves correlated; the method shares only low-dimensional outputs between agents while training local models to extract informative signals from peers, inducing a game in which each agent's loss depends on others' models, and the authors prove convergence with probability one to a globally optimal solution under a linear model despite the nonconvex global objective, with experiments on structured multi-digit MNIST tasks showing the method remains highly effective even in highly nonlinear settings.