On optimal Sampling in low and high dimension
De l' echantillonnage optimal en grande et petite dimension
Abstract
During my PhD, I had the chance to learn and work under the great supervision of my advisor R emi (Munos) in two elds that are of particular interest to me. These domains are Bandit Theory and Compressed Sensing. While studying these domains I came to the conclusion that they are connected if one looks at them trough the prism of optimal sampling. Both these elds are concerned with strategies on how to sample the space in an e cient way: Bandit Theory in low dimension, and Compressed Sensing in high dimension. In this Dissertation, I present most of the work my co-authors and I produced during the three years that my PhD lasted.
Pendant ma th ese, j'ai eu la chance d'apprendre et de travailler sous la supervision de mon directeur de th ese R emi, et ce dans deux domaines qui me sont particuli erement chers. Je veux parler de la Th eorie des Bandits et du Compressed Sensing. Je les vois comme intimement li es non par les m ethodes mais par leur objectif commun: l' echantillonnage optimal de l'espace. Tous deux sont centr es sur les mani eres d' echantillonner l'espace e cacement : la Th eorie des Bandits en petite dimension et le Compressed Sensing en grande dimension. Dans cette dissertation, je pr esente la plupart des travaux que mes co-auteurs et moi-m^eme avons ecrit durant les trois ann ees qu'a dur e ma th ese.
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