  Significant advances in edge computing capabilities enable learning to occur
at geographically diverse locations. In general, the training data needed in
those learning tasks are not only heterogeneous but also not fully generated
locally. In this paper, we propose an experimental design network paradigm,
wherein learner nodes train possibly different Bayesian linear regression
models via consuming data streams generated by data source nodes over a
network. We formulate this problem as a social welfare optimization problem in
which the global objective is defined as the sum of experimental design
objectives of individual learners, and the decision variables are the data
transmission strategies subject to network constraints. We first show that,
assuming Poisson data streams, the global objective is a continuous
DR-submodular function. We then propose a Frank-Wolfe type algorithm that
outputs a solution within a 1-1/e factor from the optimal. Our algorithm
contains a novel gradient estimation component which is carefully designed
based on Poisson tail bounds and sampling. Finally, we complement our
theoretical findings through extensive experiments. Our numerical evaluation
shows that the proposed algorithm outperforms several baseline algorithms both
in maximizing the global objective and in the quality of the trained models.
