MADSOL

Mathematics of Stochastic and Deterministic Optimization for Deep Learning

Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond

 

Abstract 

Machine learning and artificial intelligence are rising themes of research because they have been considered as one way to produce new methods for solving striking challenges in language understanding, advice finding, signal processing, fraud detection. The explosion of datascientist jobs is certainly an evidence of the societal, economic and scientific impact of artificial intelligence. The cornerstone of machine learning methods is the use of applied mathematics and in particular, statistics and optimization. These two fields of research allow to handle both the randomness of the data and its high dimensional features. Machine learning then involves the computation of hidden parameters for a system designed to make decisions for yet unseen data.

The MaSDOL project aims at developping new deterministic and stochastic methods for solving optimization tasks from data with a possibly complex geometry. We will address accelerated optimization algorithms, stochastic algorithms and sampling with errors, optimization linked to game theory and GANs and optimal transport for deep learning.

A particular emphasis is made on the analysis of deep learning approaches for generative models (GANs) and adversarial learning. In this setting, we aim to develop novel numerical methods for machine learning and to study their mathematical properties. Another expected output of the project is to implement these algorithms on challenging issues in various domains such as image analysis, bio-informatics or data processing on graphs.


Project : 2019 – 2023

 

Contact in TSE : Sébastien GADAT