DeepAI
Log In Sign Up

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

09/16/2019
by   Kaitong Hu, et al.
0

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant measure of which is shown to be the optimal control of the initial problem under mild conditions. Therefore, this system of processes can be viewed as a continuous-time numerical algorithm for computing the optimal control. As an application, this result endorses the solvability of the stochastic gradient descent algorithm for a wide class of deep neural networks.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/03/2018

A Mean-Field Optimal Control Formulation of Deep Learning

Recent work linking deep neural networks and dynamical systems opened up...
10/15/2020

Optimal control and stablilization for linear continuous-time mean-field systems with delay

This paper studies optimal control and stabilization problems for contin...
12/11/2019

Mean-Field Neural ODEs via Relaxed Optimal Control

We develop a framework for the analysis of deep neural networks and neur...
09/21/2020

Mean-field optimal control for biological pattern formation

We propose a mean-field optimal control problem for the parameter identi...
07/02/2020

Optimal control of mean field equations with monotone coefficients and applications in neuroscience

We are interested in the optimal control problem associated with certain...
03/09/2021

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

The approximation of solutions to second order Hamilton–Jacobi–Bellman (...
01/10/2019

Accelerated Flow for Probability distributions

This paper presents a methodology and numerical algorithms for construct...