### Abstract

Original language | English |
---|---|

Publisher | arXiv |

Publication status | Published - 11 Apr 2019 |

### Keywords

- math.OC
- cs.LG
- math.NA

### Cite this

*Deep learning as optimal control problems: models and numerical methods*. arXiv.

**Deep learning as optimal control problems : models and numerical methods.** / Benning, Martin; Celledoni, Elena; Ehrhardt, Matthias J.; Owren, Brynjulf; Schönlieb, Carola-Bibiane.

Research output: Working paper

}

TY - UNPB

T1 - Deep learning as optimal control problems

T2 - models and numerical methods

AU - Benning, Martin

AU - Celledoni, Elena

AU - Ehrhardt, Matthias J.

AU - Owren, Brynjulf

AU - Schönlieb, Carola-Bibiane

PY - 2019/4/11

Y1 - 2019/4/11

N2 - We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretization. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. We discuss two different deep learning algorithms and make a preliminary analysis of the ability of the algorithms to generalise.

AB - We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretization. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. We discuss two different deep learning algorithms and make a preliminary analysis of the ability of the algorithms to generalise.

KW - math.OC

KW - cs.LG

KW - math.NA

M3 - Working paper

BT - Deep learning as optimal control problems

PB - arXiv

ER -