Advanced Learning (ENSAE)

Lecture notes

Auctions and Matchings

Auctions & Matching: Learning and Approximations (3A)

Billions of auctions are run everyday, in the amazingly huge online advertisement market. They require a complete knowledge of the different mechanism, how to improve them using past data and how to learn « good/reasonable/optimal » strategies. Matchings are also nowadays already quite important (allocation of students to universities) but will certainly become more and more used on local markets.

During the 8 lectures, we will first introduce the general concept of mechanism design, and especially auctions (1st/2nd price, combinatorial, VCG) and (stable) matchings that are or can be used in practice. The main questions are their approximation, optimisation and learning based on past data in a dynamical setting. We will introduce and study the main classical tools with a specific focus on prophet inequalities and secretary problems, but also quick reminder on statistical theory, multi-armed bandits and online algorithms.

This course will be at the intersection of mathematics (statistics, optimization), computer science (complexity, approximation), and economics (strategies, equilibria and applications). Yet it should not have strong prerequisites. The evaluation will be a written exam.

At the end of this course, students will be able to :

Compute optimal strategies and design mechanisms (especially auctions and matchings)
Find the sample complexity of approximate mechanism
Design and analyse online algorithms
Prove and generalise prophet inequalities

Advanced Machine Learning (3A)

This course presents the mathematical foundations of machine learning, with a specific focus on binary classification and its statistical complexity and properties. The major algorithms and techniques (SVM, neural nets, boosting) will also be presented and discussed.
They are going to be further analyzed and implemented in practical sessions.

Introduction to Machine Learning (2A)

This course is composed of 10 small and independent lectures that each focuses on a different concept, algorithm or techniques of machine learning. At the end of the course, the students will have a broad knowledge on what is possible to do, and how, with machine learning.

Algorithms are going to be implemented during the practical sessions.

Introduction to ML (ENSAE)