8 papers
Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis
Olivier Bokanowski, Jean-François Chassagneux, Marco Scaratti +1
We study finite-horizon stochastic optimal control problems and approximate the resulting time-discrete formulation by a direct policy-learning problem over neural-network feedback…
Saddle Networks: Structure-Preserving Architectures for Convex-Concave Functions
Xavier Warin
Saddle-point models arise throughout optimization, optimal transport, robust learning, and control. In many applications, the relevant function f(x,y) is convex in x and concave in…
Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems
Samy Mekkaoui, Huyên Pham, Xavier Warin
We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Let be a label space endowed with a reference measure , a…
Fast Gaussian process inference by exact Matérn kernel decomposition
Nicolas Langrené, Xavier Warin, Pierre Gruet
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we est…
Growth model with externalities for energetic transition via MFG with common external variable
Pierre Lavigne, Quentin Petit, Xavier Warin
This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents,…
A spectral mixture representation of isotropic kernels with application to random Fourier features
Nicolas Langrené, Xavier Warin, Pierre Gruet
Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning appl…
P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
Xavier Warin
A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that t…
Representation results and error estimates for differential games with applications using neural networks
Olivier Bokanowski, Xavier Warin
We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimat…