2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
MA1  Tutorial I
May 16, 2022 10:30 AM – 12:10 PM
Location: Walter Capital (blue) Previously BDC
Chaired by Sébastien Le Digabel
1 Presentation

10:30 AM  12:10 PM
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.