The purpose of these lecture notes is to provide an introduction to the general theory of
empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities …

We consider regression with square loss and general classes of functions without the
boundedness assumption. We introduce a notion of offset Rademacher complexity that …

We show that in pool-based active classification without assumptions on the underlying
distribution, if the learner is given the power to abstain from some predictions by paying the …

We consider the random design regression model with square loss. We propose a method
that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and …

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation
(BOA). Its exponential weights include a second order refinement. The procedure is optimal …

Minimax lower bounds. Under some convexity and tail conditions, we prove minimax lower
bounds for the three problems of Kullback–Leibler aggregation: model selection, linear and …

We study random design linear regression with no assumptions on the distribution of the
covariates and with a heavy-tailed response variable. In this distribution-free regression …

Given a finite family of functions, the goal of model selection aggregation is to construct a
procedure that mimics the function from this family that is the closest to an unknown …

We present an algorithm for the statistical learning setting with a bounded exp-concave loss
in d dimensions that obtains excess risk $ O (d\log (1/δ)/n) $ with probability $1-δ $. The core …

In the problem of aggregation, the aim is to combine a given class of base predictors to
achieve predictions nearly as accurate as the best one. In this flexible framework, no …