10h30 - 12h10
Stochastic Nonlinear Least-Squares Methods with Application to Data Assimilation and Machine Learning
Levenberg-Marquardt and trust-region methods are two well-established paradigms to tackle nonlinear least-squares problems. Most applications related to inverse problems and machine learning are naturally least-squares 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 least-squares problems. Then, I will describe a stochastic Levenberg-Marquardt framework to solve stochastic nonlinear least-squares 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 Levenberg-Marquardt approach in the context of data assimilation and machine learning.