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Significant advances in edge computing capabilities enable learning to occurat geographically diverse locations. In general, the training data needed inthose learning tasks are not only heterogeneous but also not fully generatedlocally. In this paper, we propose an experimental design network paradigm,wherein learner nodes train possibly different Bayesian linear regressionmodels via consuming data streams generated by data source nodes over anetwork. We formulate this problem as a social welfare optimization problem inwhich the global objective is defined as the sum of experimental designobjectives of individual learners, and the decision variables are the datatransmission strategies subject to network constraints. We first show that,assuming Poisson data streams, the global objective is a continuousDR-submodular function. We then propose a Frank-Wolfe type algorithm thatoutputs a solution within a 1-1/e factor from the optimal. Our algorithmcontains a novel gradient estimation component which is carefully designedbased on Poisson tail bounds and sampling. Finally, we complement ourtheoretical findings through extensive experiments. Our numerical evaluationshows that the proposed algorithm outperforms several baseline algorithms bothin maximizing the global objective and in the quality of the trained models.

Experimental Design Networks: A Paradigm for Serving Heterogeneous Learners under Networking Constraints