Journées de l'optimisation 2022
HEC Montréal, Québec, Canada, 16 — 18 mai 2022
MA1  Tutorial I
16 mai 2022 10h30 – 12h10
Salle: Walter Capital (bleu) Anciennement BDC
Présidée par Sébastien Le Digabel
1 présentation

10h30  12h10
Stochastic Nonlinear LeastSquares Methods with Application to Data Assimilation and Machine Learning
LevenbergMarquardt and trustregion methods are two wellestablished paradigms to tackle nonlinear leastsquares problems. Most applications related to inverse problems and machine learning are naturally leastsquares problems, but with noisy estimates. The presence of noise is often due to the estimation of the objective function and/or its derivatives via cheaper or less accurate procedures.
In this talk, I will first present classical methods used to solve deterministic nonlinear leastsquares problems. Then, I will describe a stochastic LevenbergMarquardt framework to solve stochastic nonlinear leastsquares problems. Provided that the estimates are accurate, with some probability, I will give also bounds on the expected number of iterations needed to reach an approximate stationary point. My talk will be concluded by illustrating the stochastic LevenbergMarquardt approach in the context of data assimilation and machine learning.