The Nested Distance is a distance between scenario trees (stochastic processes which are discrete in both space and time) introduced by Pflug and Pichler in 2012 as a refinement of the Wasserstein distance suited for multistage optimization problems. In this presentation, I will make recalls on discrete optimal transport, explain its link with the Wasserstein distance and prove how the Nested Distance is a better tool for multistage optimization purposes. Then I will show how regularized optimal transport allows one to fast compute an approximation of the Nested Distance while retaining its main properties. Lastly, I will present the problem of scenario tree reduction and its relationship with the Nested Distance. The presentation will be in English.
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Benoît Tran is a former graduate of Université Paris-Saclay in France. He did his Ph.D. in both Ecole Polytechnique and Ecole des Ponts ParisTech on stochastic optimal control. Since 2021, he is a post doctoral researcher at FGV EMap under the supervision of Prof. Vincent Guigues to work on subjects related to multistage stochastic optimization.