The dynamic programming approach applied to stochastic control problems allows one to find optimal feedback policies but it requires solving a nonlinear equation or a fully nonlinear partial differential equation of Hamilton-Jacobi type over the state space. Hence, this method suffers from the curse of dimensionality, for instance grid-based methods like finite-difference or finite element methods have a complexity exponential in the dimension of the state space.
Several methods were created to bypass this difficulty by assuming some structure on the problem. Examples are the max-plus based method of McEneaney and the stochastic dual dynamic programming (SDDP) algorithm of Pereira and Pinto.
We aim to associate and compare these methods in order to solve more general structures, namely problems involving a finite set-valued (or switching) control and a continuum-valued control, knowing that the value function associated to a fixed switching strategy is convex.
I am a former student of Paris-Sud University. There I studied mathematics for several years, succeeded in getting the agrégation of mathematics (competitive national examination for teachers) in 2016 and specialized in optimization the following year.
I did a 4 months internship hosted by the LAAS-CNRS under the supervision of Jean-Bernard Lasserre and Edouard Pauwels about the computation of the empirical Christoffel function and its uses in outlier detection. The manuscript (in french). More info can be found on my LinkedIn page.
CERMICS, École Nationale des Ponts et Chaussées
6 et 8, av. Blaise Pascal
Cité Descartes - Champs-sur-Marne
77455 Marne-la-Vallée Cedex 2