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 12 to Feb 9 + Wednesday Feb 8, 9.45am-1pm.
    Where? all lectures will take place in the room Fokko-du-Cloux of the Braconnier building at the Lyon1 campus La Doua, except for the lectures of Wed Feb 8, which will be in the room 101 of the Quai 43 building (same campus).
    Language: the course will be given in English in case at least one student prefers so, which we expect.
    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 12 and 19, 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 26 and Feb 2, given by N. Bonneel, each class includes a practical computer session): the Sinkohrn algorithm; the sliced Wasserstein distance.
  • Lectures 5 and 6 (Feb 8 and 9, given by I. Redko, each class includes a practical computer session): transfer learning and style transfer.

    • 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 and the beginning of Section 1.3 of OTAM.
    Precise references for lecture 2: see Sections 1.6.2, 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 (scheduled for March 29th) and a grade for each practical session.

    Text and corretion of the written exam.