报告题目：Primal Parallel Heuristics for Computing Wasserstein Barycenters
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The Wasserstein Barycenter of a given set of (discrete)probability measures is defined as a (discrete) probability measure that minimizes the sum of the pairwise Wasserstein distances between the barycenter itself and each input measure. The computation of a Wasserstein Barycenter can be formulated as a Linear Programming problem over the space of discrete probability measures. The exact solution of the Wasserstein Barycenter problem is, in general, NP-hard due to the size of the problem instance, which grows exponentially in the number of input measures. In this talk, we review existing numerical methods for computing Wasserstein Barycenters between discrete probability distributions. In particular, we present simple but efficient primal iterative heuristics, which exploit the interpolation properties of an optimal transportation plan obtained while computing the exact Wasserstein Distance of order 2 between a pair of measures. To evaluate the proposed primal heuristics, we report on extensive computational tests using random Gaussian distributions, the MNISThandwritten digit dataset, and the Fashion MNIST. The computational results show that the proposed primal heuristic yields an average optimality gap significantly smaller than 1% in a very short runtime compared with other state-of-the-art algorithms.
Stefano Gualandi is an Associate Professor at the Department of Mathematics of the University of Pavia, where he leads the Computational Optimization Research Group. His expertise is in computational optimization for combinatorial problems and in integrating numerical methods from operations research and artificial intelligence. He has applied these methods to academic and industrial problems and has published more than forty peer-reviewed papers in international journals and conference proceedings. He received a Distinguished Paper Award at the international conference on Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR) in 2020. He received an M.S. degree in computer engineering from the University of Pavia in 2002, a second M.S. degree in Artificial Intelligence from the Katholieke Universiteit Leuven (KUL), Belgium, and he got a Ph.D. degree in Operations Research from the Politecnico di Milano in 2008.
From 2016 to 2019 he left academia to join AntOptima, a spinoff of the “Istituto Dalle Molle di Studi sull'Intelligenza Artificiale“ (IDSIA), where he worked as a work-package leader for a European Research project. While working at AntOptima, he developed professional optimization codes for several worldwide customers, such as, for instance, Volkswagen, Shell, Eni, and Tamoil.
He currently serves as associate editor of INFORMS Journal on Computing and as a Senior Program Committee member for the AAAI international conference. He regularly serves on the technical program committee of major international conferences (NeurIPS, ICML, AAAI, IJCAI, CPAIOR, CP). He is currently involved in the scientific and technical activities of several national and European research projects, and he leads several industrial projects.