Transport Optimal pour l'Apprentissage

Master 2 Maths en Action (parcours apprentissage) et Master 2 Mathématiques Avancées (parcours probabilité)

This course if given by
  • Filippo Santambrogio (ICJ, Lyon)
  • Nicolas Bonneel (LIRIS, Lyon)
  • Ievgen Redko (Noah's Ark Lab, Huawei)

    • Practical Information

    Duration: 18h
    When? Thursday 9am-12.15pm from Jan 11 to Feb 8 + Wednesday Jan 24, 9am-12.15pm.
    Where? all lectures will take place in the room Séminaire 1 of the basement of the Braconnier building at the Lyon1 campus La Doua.
    Language: the course could be given in English in case at least one student prefers so, but so far it's in French.
    Examination: Contrôle continu (evaluation of the practical sessions) + Contrôle terminal (a short written exam after the end of the end of the course, based on the theoretical part).

    Program

    There will be 6 classes of 3h each. The program is more or less the following.

  • Lectures 1 and 2 (Jan 11 and 18, given by F. Santambrogio): the main theoretical basis of OT (Monge and Kantorovich problems, existence of optimal plans, duality, existence of optimal maps,cyclical monotonicity, the 1D case, Wasserstein distances, geodesics and barycenters in the Wasserstein spaces).
  • Lectures 3 and 4 (Jan 24 and 25, given by I. Redko, each class includes a practical computer session): transfer learning and style transfer.
  • Lectures 3 and 4 (Feb 1 and 8, given by N. Bonneel, each class includes a practical computer session): the Sinkohrn algorithm; the sliced Wasserstein distance.

    • References:

    All the material covered in the course lectures 1 and 2 is contained in the book Optimal Transport for Applied Mathematicians (OTAM, see here or here for a non-official version).
    Of course, there are more classical references, such as the first book by Cédric Villani Topics in Optimal Transportation (Am. Math. Soc., GSM, 2003)

    Precise references for lecture 1: see Sections 1.1, 1.2, the beginning of Section 1.3, and Section 1.6.2 of OTAM.
    Precise references for lecture 2: see Sections 2.2, 3.1.1, 5.1, 5.2, 5.4, 5.5.5 of OTAM.

    Exam

    The course wil be evaluated through a written exam on the first part and a grade for each practical session.

    Text and correction of the written exam given in 2023.