Approximation stochastique et apprentissage en ligne // Stochastic Approximation: Theory and Applications to Online Learning

(voir description en anglais)
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Stochastic approximation (SA) is a widely used algorithmic paradigm for solving fixed-point equations or optimization problems when only noisy observations are available. Introduced in the 1950s by Robbins and Monro, SA remains central to many modern algorithmic approaches in statistics, optimization, and machine learning. Fundamentally, a stochastic approximation algorithm aims to generate a sequence of estimates $\theta_n$ that converges to a target $\theta^*$—typically a solution to a root-finding problem or a minimizer of an expected loss—based on noisy observations of gradient-like information. SA forms the theoretical backbone of several key algorithmic classes in machine learning, including stochastic gradient descent (SGD), temporal-difference learning, $Q$-learning, and policy gradient.

The primary objective of this thesis is to advance the theoretical understanding of stochastic approximation schemes, with a focus on characterizing the error between the iterates $\theta_n$ and their limiting point $\theta^*$—especially in the presence of \emph{multi-scale dynamics}
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Début de la thèse : 01/10/2025

Concours allocations

Université Grenoble Alpes

217 MSTII - Mathématiques, Sciences et technologies de l'information, Informatique

Master en informatique ou mathématique appliqué. Forte appétence pour l'apprentissage statistique. Cours avancé de probabilité et de processus stochastique.
Master in applied mathematics or computer science. Good knowledge of applied probability and stochastic processes. Will to work on online learning and optimization.