Journées de l'optimisation 2022

HEC Montréal, Québec, Canada, 16 — 18 mai 2022

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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 Least-Squares Methods with Application to Data Assimilation and Machine Learning

    • Youssef Diouane, prés., Polytechnique Montréal

    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.