18 citations · 37 across the 6 of their papers we have counts for
9 papers
Actor-Critic learning for mean-field control in continuous time
Noufel Frikha, Maximilien Germain, Mathieu Laurière +2
We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a…
A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection
Maximilien Germain, Huyên Pham, Xavier Warin
We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of t…
DeepSets and their derivative networks for solving symmetric PDEs
Maximilien Germain, Mathieu Laurière, Huyên Pham +1
Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient nume…
Rate of convergence for particle approximation of PDEs in Wasserstein space
Maximilien Germain, Huyên Pham, Xavier Warin
We prove a rate of convergence for the -particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or…
Neural networks-based algorithms for stochastic control and PDEs in finance
Maximilien Germain, Huyên Pham, Xavier Warin
This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic…
Approximation error analysis of some deep backward schemes for nonlinear PDEs
Maximilien Germain, Huyen Pham, Xavier Warin
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance…
Numerical resolution of McKean-Vlasov FBSDEs using neural networks
Maximilien Germain, Joseph Mikael, Xavier Warin
We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate…
Neural networks-based backward scheme for fully nonlinear PDEs
Huyen Pham, Xavier Warin, Maximilien Germain
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction…
A numerical scheme for stochastic differential equations with distributional drift
Tiziano De Angelis, Maximilien Germain, Elena Issoglio
In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negati…