MoKaMeeting du 11 avril 2018 . Arnak Dalalyan (ENSAE – CREST) / User-friendly guarantees for the Langevin Monte Carlo

Le prochain séminaire de l’équipe Mokaplan aura lieu le mercredi 11 avril à 10h30 à l’INRIA Paris (rue du Charolais) en salle A415.

Nous aurons le plaisir d’écouter Arnak Dalalyan (ENSAE – CREST):

Titre: User-friendly guarantees for the Langevin Monte Carlo

Abstract: In this talk, I will revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. I will discuss the existing results when the accuracy of sampling is measured in the Wasserstein distance and provide further insights on relations between, on the one hand, the Langevin Monte Carlo for sampling and, on the other hand, the gradient descent for optimization. I will also present non-asymptotic guarantees for the accuracy of a version of the Langevin Monte Carlo algorithm that is based on inaccurate evaluations of the gradient. Finally, I will propose a variable-step version of the Langevin Monte Carlo algorithm that has two advantages. First, its step-sizes are independent of the target accuracy and, second, its rate provides a logarithmic improvement over the constant-step Langevin Monte Carlo algorithm.

This is a joint work with A. Karagulyan​

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