Clôture du séminaire des (post)doctorant(es)

- Axel Renard : (2:00pm)

Titre : Méthodes Hilbertiennes en analyse complexe.

- Adrienne Tuynman: (3:00pm)

Title: Finding good policies in average-reward reinforcement learning.

Abstract: As reinforcement learning garners more and more interest worldwide,
algorithms grow bigger and better. However, what a "good'' algorithm is
can depend on the speaker, as the optimality and speed of an algorithm
can be measured in many different ways. I will present the motivation
for aiming towards average-reward best policy identification algorithms.
I will then present the existing results in that setting, to identify
how to accurately measure the (minmax) complexity of a given instance.
If we have time, we will also address the problem-dependent complexity
of the problem by wondering how much information is strictly necessary
to draw correct conclusions.

- Nicola Carissimi: (4:30pm)

Title: 2-categories, adjunctions and graphical calculus.

Abstract: It is common in category theory to deal with "morphisms between morphisms" (or 2-morphisms), since that is what we have with natural transformations, which are morphisms between functors, e.g.morphisms between morphisms of categories. All this structure can be encoded in the notion of a 2-category, and many concept turn to have a new place where to be studied. Among these, one of the most enjoyable is the concept of adjunction. We will explain these concepts and appreciate how they really are "just" 2-categorical.

One problem with the introduction of all this higher level maps is very practical, and related to the way of dealing with (fastly becoming huge and 3-dimensional) compositions of 2-morphisms. It becomes then a crucial matter having a clean and intuitive way of representing these creatures, and that is where string diagrams arise (though the history is not that linear and much more interdisciplinary that it may seem!) We will describe their functioning, and if time permits, we will see an application.