PAC-Bayesian aggregation and multi-armed bandits

Abstract

This habilitation thesis presents several contributions to (1) the PAC-Bayesian analysis of statistical learning, (2) the three aggregation problems: given d functions, how to predict as well as (i) the best of these d functions (model selection type aggregation), (ii) the best convex combination of these d functions, (iii) the best linear combination of these d functions, (3) the multi-armed bandit problems.

References in corpus (13)

• Consistency of the group Lasso and multiple kernel learning
• High-dimensional additive modeling
• 2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization
• Fast learning rates for plug-in classifiers
• Risk bounds for statistical learning
• Empirical Bernstein Bounds and Sample Variance Penalization
• Bandit Algorithms for Tree Search
• From $\epsilon$-entropy to KL-entropy: Analysis of minimum information complexity density estimation
• Sparse Regression Learning by Aggregation and Langevin Monte-Carlo
• Fast learning rates in statistical inference through aggregation
• PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers
• Risk bounds in linear regression through PAC-Bayesian truncation
• High confidence estimates of the mean of heavy-tailed real random variables

Cited by in corpus (1)

• Fast rates in learning with dependent observations