8 papers
Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data
Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1
This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic d…
Policy Gradient for Continuous-Time Mean-Field Control
Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1
This paper develops a policy gradient method for entropy-regularized mean-field control in the discounted infinite-horizon setting. We consider randomized feedback policies and a c…
Convergence, design and training of continuous-time dropout as a random batch method
Antonio Ãlvarez-López, MartÃn Hernández
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the compu…
Random domain decomposition for parabolic PDEs on graphs
MartÃn Hernández
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require consider…
Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks
MartÃn Hernández, Enrique Zuazua
We present a fully constructive analysis of deep ReLU neural networks for classification and function approximation tasks. First, we prove that any dataset with distinct points…
Random Batch Methods for Discretized PDEs on Graphs
MartÃn Hernández, Enrique Zuazua
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically deman…