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Sholom SCHECHTMAN (UPEM – Télécom Paris) – “The ODE method in Optimization. Application to the convergence of stochastic subgradient descent for non-smooth and non-convex functions”

February 24, 2:00 pm - 3:00 pm

The Statistics-Econometrics-Machine Learning Seminar.

Time: 14:00 pm – 15:00 pm
Date: 24th of February 2021
Place: Online (Click here to join the seminar on Zoom)

Sholom SCHECHTMAN (UPEM – Télécom Paris) – “The ODE method in Optimization. Application to the convergence of stochastic subgradient descent for non-smooth and non-convex functions”

Abstract :

The ODE method associates to an optimization algorithm its continuous counterpart: an ordinary differential equation (ODE).
Following the work of Benaim, under mild conditions the iterates of the algorithm will then shadow a solution to the ODE. As an application we will show the convergence of the stochastic gradient descent for a smooth (non-convex) function to its critical points.
In the second part of the talk, following the work of Benaim, Hofbauer and Sorin, an extension to differential inclusions will be presented, and as a consequence a simple proof of convergence of the stochastic subgradient descent for a non-smooth and non-convex function to its critical points.

Sponsors:
CREST

Details

Date:
February 24
Time:
2:00 pm - 3:00 pm
Event Categories:
, ,
Website:
https://statecoml.github.io

Venue

online
5, avenue Henry Le Chatelier
91120 Palaiseau, France

Organizers

Martin Mugnier
François-Pierre Paty
Nicolas Schreuder