I am interested in providing a theoretical framework for Sequential decision making and
Reinforcement learning. For this reason, I mostly play with Bandit theory but not only. This needs
understanding properties of empirical processes for small number of samples that can or can not be
learned and at which speed. In particular, I am interested in transferring/developping tools from mathematical Statistics to the field of Machine Learning and especially Sequential Learning:
- Sequential Learning theory:
This is a very motivating field of research that adresses the following kind of problems (amongst others): Let consider you have on one hand several statistical processes indexed by time, and on the other hand a property P. Then one typical goal is to detect which one satisfies the property P as soon as possible, i.e. optimally and non-asymptotically. Thus, this field of research is deeply related to:
- Empiricial processes theory.
- Non-asymptotic statistics.
- Information and Coding theory.
- Optimal Stopping theory.
- Statistical theory:
Of course since we need to understand the objects we consider, statistical theory is fundamental. For instance, there are many concentration/large deviation results that are still not understood optimally, like for instance concentration involving the empirical distribution (and not only empirical mean), or concentration of high order moments. There are many others important and difficult questions involving model selection, covershift, sparsity, optimal sensing, empirical penalization, active covering... that are still not solved, especially when we ask for adaptivity.
Here are some random topics I like to read about, with my corresponding mathematical "Heroes":
- Metamorphosis, flux, current, etc (see A. Trouve)
- KMT strong approximation theory (see P. Berthet)
- PAC-Bayes analysis and oracle inequalities (see O. Catoni)
- Sparsification networks (see S. Mallat)
- Optimal transport (see C. Villani)
I am more an more interested in:
- Manifolds and especially stochastic manifolds, which is related to Geometry of Information theory,
- Weakly-differentiable manifolds (with shocks) from a probabilistic/statistical point of view.
and also: Jazz (Saxophone), Archery, Historical foundation of myths, legends and beliefs, Elvian languages...
Here is an illustration of research:
"La première image illustre la quête de la vérité, la bataille, la fougue intellectuelle habitant le chercheur, pour aller vers son but, symbolisé par la troisième image. Celle-ci illustre l'apaisement intellectuel, le bonheur ressenti lors de la découverte d'un théorème, la contemplation du beau et du vrai, l'objet de la quête enfin. En ce sens le chercheur est un chevalier. La deuxième image relie ces deux mondes, par l'intermédiaire de ce clown hirsute ouvrant les bras. C'est ainsi que l'artiste expose tout son art. Ce clown est l'incarnation de la démarche scientifique, décalée, osant les idées les plus folles, et nécessitant l'émotion la plus productive pour accomplir sa tâche: le rire. Ce clown sans le sou traduit également l'humilité du chercheur, et le détachement des choses matérielles. Ainsi va le chercheur, chevalier, clown et artiste à la fois."
As every researcher knows, there is generally an important gap between all what we know/master about, all what we are interested in and what finally appears scarcely in some of our published papers. Sometimes it may also be challenging to find people to work with on some specific topic that is a bit off your main research stream. So here I want to list some topics/keywords/questions I would love working on. Some are kind of linked to my field, some are definitely not, sometimes I manage to work on them a little bit, often I am just too busy with another exciting project.The purpose of this list is that you, as a researcher or a student, get in touch with me about one topic so that we can start collaborating on this together. If you feel like being interested by one of these projects, feel free to contact me, and I would be happy to guide you more.
Natural Language Optimization:
The idea of the project is to combine computation of co-articulation complexity measure from a 3d model of a speech apparatus together with a grammar generator that is able to approximate most natural languages (up to grammatical exception rules resulting from co-articulation shortcuts) and a corpus of training documents. The goal is to generate a new natural language that minimizes the co-articulation complexity of most frequent grammatical structures while ensuring that the phoneme distance (geodesic distance in the 3d model of speech apparatus) between two grammatical structures increases with their co-occurrence frequency. We can start with a stable language with little exceptions (that is, has a simple grammar), such as antique Latin.
The idea of the project is to study the notion of shock between "particles" occurring in some physical world from a purely geometric point of view. Identifying particles with propagation equations in a manifold describing the physical world, it is natural, due to the loss of differentiability of trajectories that occurs in case of a shock, to study a corresponding notion of weakly-differentiable manifold in order to describe the physical world intrinsically. This requires redefining most of the usual objects of differentiable geometry, such as the tangent space, the notion of geodesics, curvature, transport, currents, streams, etc. The goal of the project is to extend the standard objects of differentiable geometry to the weakly-differentiable case, and provide (statistical?) interpretations in simplest cases such as a one-dimensional space.
Information reconstruction in resource networks:
In this project, we study a large network of agents who produce, transfer and consumate resources. Only transfer of resources can be observed but neither production nor consumptions. Under some assumptions such that a production can only start if the resources needed for production have been received by the agent, and that transfer of resources systematically occur when a production cannot start, the goal is to study to which point it is possible to reconstruct the information of production and consumption, with quantitive bounds, as well as the network of effective dependency of a specific production.
There are also other projects, and many more, such as:
Automatic music composer.