8 papers
Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data
Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1
This paper develops a model-free framework for continuous-time mean-field control when the population evolves according to unknown controlled McKean--Vlasov dynamics and only discr…
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 Álvarez-López, Martín Hernández
We study continuous-time dropout in controlled differential equations. We introduce a random-batch approximation of additive vector fields. On each time interval of length , a r…
Random domain decomposition for parabolic PDEs on graphs
Martín 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…
Random Batch Methods for Discretized PDEs on Graphs
Martin Hernandez, Martín Hernández, Enrique Zuazua
Diffusion and transport processes on networks arise in applications such as pipeline systems, traffic and information flow, and energy and thermal networks. In these settings the d…
Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks
Martín 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…
Mini-batch descent in semiflows
Alberto Domínguez Corella, Martín Hernández
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-b…
Averaged observations and turnpike phenomenon for parameter-dependent systems
Martín Hernández, Martin Lazar, Sebastián Zamorano
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations i…