UE Convex and distributed optimization

Degrees incorporating this pedagocial element :

Description

Courses: (4 parts of 3h each + 3 hours practical work)

  1. Introduction to convex optimization: concepts in convex analysis (duality, proximal operators), how to identify potential difficulties in optimization problems. Illustrations in supervised learning (classification and regression problems) and in operation research (decomposition methods).
  2. Algorithms in convex optimization (gradient, proximal gradient, conditional gradient, ADMM)
  3. Introduction to distributed computation (architectures for computation, map-reduce scheme, MPI, Spark) + 3h practical work
  4. Distributed optimisation algorithms, stochastic algorithms, asynchronous methods.

Practical work (2 parts of 6h each)

  1. application to a recommendation system
  2. sparse logistic regression in high dimension

Evaluation :

The final grade is the mean between the grade on the report on the practical sessions and the grade of the presentation of a recent research article.

Prerequisites

The students should have basic knowledge on applied maths (matrix,functions,…) and on statistic and probability (expectation, variance,…). A first experience with optimisation is also required; the refresher course on matrix analysis and optimisation, proposed at the beginning of the semester, covers the necessary starting material. The students should also have programming skills. The tutorial on machines will be using Python notebooks.