Online learning, links with optimization and games


Université Paris–Saclay — 2025–2026
Thursdays 9:00–12:15 — Room 1A7

This course proposes a unified presentation of regret minimization for adversarial online learning problems, and its application to various problems such as Blackwell's approachability, optimization algorithms (GD, Nesterov, SGD, AdaGrad), variational inequalities with monotone operators (Mirror-Prox, Dual Extrapolation), fixed-point iterations (Krasnoselskii-Mann), and games. The presentation aims at being modular, so that introduced tools and techniques could easily be used to define and analyze new algorithms.

Schedule

January, 22th
Convexity tools — Exercices
January, 29th
UMD Theory — Exercices
February, 5th
Online linear optimization — Exercices
February, 12th
Online convex optimization — Exercices
February, 19h
Blackwell's approachability — Exercices
March, 12th
Gradient methods in optimization & AdaGrad
March, 19th
Regret learning in games
March, 26th
Extensive-form games

Evaluation

Evaluation will be 100% project-based.

Projects will become available progressively. A project can be attributed to at most one student. You must choose a project below (first come, first served) and notify me by sending an e-mail.

Projects have various levels of estimated difficulty, indicated by a number of stars. Grading will take that into account. If you are facing important difficulties, you can ask for help by sending me an e-mail.

Completed work must be sent by e-mail and may contain several files (e.g. a pdf and a Jupyter notebook).

If you need your grade early (for e.g. applications), you can send your project one week before the date on which you need your grade.

Available projects

Candidates for validation

  1. Camilli, Petra — ★★ [theory] A finer analysis for convex optimization with step-sizes
  2. Delbreil, Elisa — ★★★ [theory, code] Approachability algorithms based on time-dependent norms
  3. Jiang, Bingjian — ★★ [theory, code] UMD-based extension of AdaGrad-Norm and application to games
  4. Luo, Xiangyu — ★★ [theory, code] A generalized approach for nonsmooth convex optimization
  5. Mas, Fanny — ★★ [theory] AdaGrad-Diagonal: Stronger adaptivity to smoothness
  6. Melan, David — ★★★ [theory, code] Approachability-based optimization
  7. Pefura Yone, Eric — ★★ [theory] Composite optimization
  8. Ren, Fangdu — ★ [theory, code] A hybrid of mirror descent and dual averaging
  9. Villeroy de Galhau, Gaspard — ★★ [theory] AdaGrad with normalization
  10. Yuan, Hongyi — ★★ [theory] Dual averaging variants of AdaGrad
  11. Benedicto Plagnes, Hugo — ★★★ [theory, code] Variants of AdaGrad-Norm and application to games