Fetching the paper…

Reading the bibliography…

2019

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

Hu, Kaitong, Kazeykina, Anna, Ren, Zhenjie

Original
PDF
Post on X

Understand

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.

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

Built on

V. G. Boltyanskii, R. V. Gamkrelidze, and L. S. Pontryagin
1960
Earlier work this paper cites.
A. E. Bryson and W. F. Denham
1962
Earlier work this paper cites.
S. K. Mitter
1966
Earlier work this paper cites.
W. H. Fleming
1977
Earlier work this paper cites.
D. Henry
1981
Earlier work this paper cites.
H. Föllmer
1986
Earlier work this paper cites.
N. El Karoui, D. Nguyen, and M. Jeanblanc-Picqué
1987
Earlier work this paper cites.
Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski
1988
Earlier work this paper cites.
K. Hornik
1991
Earlier work this paper cites.

Similar

B. A. Pearlmutter
Original
1995
Cited alongside, same era.
P. Dupuis and R. S. Ellis
1997
Cited alongside, same era.
S. Hochreiter and J. Schmidhuber
1997
Cited alongside, same era.
R. Jordan, D. Kinderlehrer, and F. Otto
1998
Cited alongside, same era.
F. Otto and C. Villani
2000
Cited alongside, same era.
A. Krizhevsky, I. Sutskever, and G. E. Hinton
2012
Cited alongside, same era.
J. Ma, Z. Wu, D. Zhang, and J. Zhang
2015
Cited alongside, same era.

Then

S. Mei, A. Montanari, and P.-M. Nguyen
2018
Later among the works it cites.
R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. Duvenaud
Original
2019
Closest in time.
C. Cuchiero, M. Larsson, and J. Teichmann
Original
2019
Closest in time.
W. E, J. Han, and Q. Li
2019
Closest in time.
A. Eberle, A. Guillin, and R. Zimmer
2019
Closest in time.
K. Hu, Z. Ren, D. Siska, and L. Szpruch
Original
2019
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

A. Eberle

2016

Cited alongside, same era.

K. He, X. Zhang, S. Ren, and J. Sun

2016

Cited alongside, same era.

G.-H. Liu and E. A. Theodorou

2019

Closest in time.

H. Liu and P. Markowich

2019

Closest in time.

S. Mei, T. Misiakiewicz, and A. Montanari

2019

Closest in time.