Optimal transport (OT) and Wasserstein barycenters have emerged as powerful tools in machine learning, signal processing, and statistics. This talk explores recent advances in the decentralized computation of OT and barycenters over networks. We present algorithmic contributions spanning accelerated primal-dual methods, novel quantization schemes for communication-efficient optimization, and equitable formulations that ensure fairness in distributed cost sharing. In particular, we highlight methods for semi-discrete entropy-regularized barycenter computation, the use of probability-proportional-to-size quantization to reduce communication loads, and a decentralized algorithm for equitable OT that matches centralized iteration complexity while ensuring fairness. These results collectively illustrate how principled optimization and stochastic approximation methods can enable scalable, decentralized solutions for high-dimensional transport problems.
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