DeepAI AI Chat
Log In Sign Up

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations

03/09/2021
by   Philipp Grohs, et al.
0

The approximation of solutions to second order Hamilton–Jacobi–Bellman (HJB) equations by deep neural networks is investigated. It is shown that for HJB equations that arise in the context of the optimal control of certain Markov processes the solution can be approximated by deep neural networks without incurring the curse of dimension. The dynamics is assumed to depend affinely on the controls and the cost depends quadratically on the controls. The admissible controls take values in a bounded set.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/16/2019

Mean-field Langevin System, Optimal Control and Deep Neural Networks

In this paper, we study a regularised relaxed optimal control problem an...
01/30/2020

Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs

We demonstrate that deep neural networks with the ReLU activation functi...
08/28/2020

Control On the Manifolds Of Mappings As a Setting For Deep Learning

We use a control-theoretic setting to model the process of training (dee...
04/29/2022

A weighted first-order formulation for solving anisotropic diffusion equations with deep neural networks

In this paper, a new weighted first-order formulation is proposed for so...
11/02/2016

Deep Learning Approximation for Stochastic Control Problems

Many real world stochastic control problems suffer from the "curse of di...
11/04/2021

A control method for solving high-dimensional Hamiltonian systems through deep neural networks

In this paper, we mainly focus on solving high-dimensional stochastic Ha...
12/12/2022

On an Interpretation of ResNets via Solution Constructions

This paper first constructs a typical solution of ResNets for multi-cate...