Collaborative Learning for Large-Scale Discrete Optimal Transport under Incomplete Populational Information

Optimal transport (OT) is a framework that allows for optimal allocation of limited resources in a network consisting of sources and targets. The standard OT paradigm does not extend over a large population of different types. In this paper, we establish a new OT framework with a large and heterogeneous population of target nodes. The heterogeneity of targets is described by a type distribution function. We consider two instances in which the distribution is known and unknown to the sources, i.e., transport designer. For the former case, we propose a fully distributed algorithm to obtain the solution. For the latter case in which the targets' type distribution is not available to the sources, we develop a collaborative learning algorithm to compute the OT scheme efficiently. We evaluate the performance of the proposed learning algorithm using a case study.