## 2 événements

• Mathématiques de l’apprentissage

### Lundi 6 mai 12:30-13:30 - Bezirgen Veliyev - Aarhus University

Functional sequential treatment allocation

Résumé : In this paper we study a treatment allocation problem with multiple treatments, in which the individuals to be treated arrive sequentially. The goal of the policy maker is to treat every individual as well as possible. Which treatment is “best’’ is allowed to depend on various characteristics (functionals) of the individual-specific outcome distribution of each treatment. For example measures of welfare, inequality, or poverty. We propose the Functional Sequential Allocation policy, and provide upper bounds on the regret it incurs compared to the oracle policy that knows the best treatment for each individual. These upper bounds increase sublinearly in the number of treatment assignments and we show that this regret guarantee is minimax optimal. In addition, the assumptions under which this regret guarantee is established are as weak as possible—even a minimal weakening of them will imply non-existence of policies with regret increasing sub-linearly in the number of assignments.
Link for the preprint : https://arxiv.org/pdf/1812.09408.pdf

Lieu : Salle 106, bâtiment 1R1

• Séminaire d’Analyse Réelle

### Lundi 6 mai 14:00-15:00 - Matteo Levi - Università di Bologna & Universitat Autònoma de Barcelona

The Dirichlet problem on infinite trees

Résumé : Trees in analysis are both a fruitful model for continuous problems and an interesting metric space per se. In this talk, we consider the Dirichlet problem on a locally finite rooted tree of infinite depth, and we prove that the set of irregular points for continuous boundary data has zero capacity. We also give some uniqueness results for solutions in Sobolev $W^{1,p}$ of the tree. The talk is based on a joint work with Nikolaos Chalmoukis. We will also mention and use some results previously obtained with Nicola Arcozzi.

Lieu : Salle Picard (Bat 1R2 Salle 129)