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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