**Abstract: **

Machine learning algorithms are ubiquitous in most scientific, industrial and personal domains, with many successful applications. As a scientific field, machine learning has always been characterized by the constant exchanges between theory and practice, with a stream of algorithms that exhibit both good empirical performance on real-world problems and some form of theoretical guarantees. Many of the recent and well publicized applications come from deep learning, where these exchanges are harder to make, in part because the objective functions used to train neural networks are not convex. In this talk, I will present recent results on the global convergence of gradient descent for some specific non-convex optimization problems, illustrating these difficulties and the associated pitfalls (joint work with Lénaïc Chizat and Edouard Oyallon)

**Bio:**

Francis Bach is a researcher at INRIA, leading since 2011 the SIERRA project-team, which is part of the Computer Science Department at Ecole Normale Supérieure, and a joint team between CNRS, ENS and INRIA. Since 2016, he is an adjunct Professor at Ecole Normale Supérieure. He completed his Ph.D. in Computer Science at U.C. Berkeley, working with Professor Michael Jordan, and spent two years in the Mathematical Morphology group at Ecole des Mines de Paris, he then joined the WILLOW project-team at INRIA/Ecole Normale Superieure/CNRS from 2007 to 2010. He obtained in 2009 a Starting Grant and in 2016 a Consolidator Grant from the European Research Council, and received the INRIA young researcher prize in 2012, the ICML test-of-time award in 2014, as well as the Lagrange prize in continuous optimization in 2018. In 2015, he was program co-chair of the International Conference in Machine learning (ICML), and general chair in 2018; he is now co-editor-in chief of the Journal of Machine Learning Research. Francis Bach is primarily interested in machine learning, and especially in graphical models, sparse methods, kernel-based learning, large-scale convex optimization, computer vision and signal processing