LPGD: A General Framework for Backpropagation through Embedded
Optimization Layers

D 2024

LPGD: A General Framework for Backpropagation through Embedded Optimization Layers

PAULUS, Anselm; Georg MARTIUS a Vít MUSIL

Základní údaje

Originální název

LPGD: A General Framework for Backpropagation through Embedded Optimization Layers

Autoři

PAULUS, Anselm (276 Německo); Georg MARTIUS (276 Německo) a Vít MUSIL (203 Česká republika, garant, domácí)

Vydání

235. vyd. Neuveden, Proceedings of Machine Learning Research, od s. 39989-40014, 26 s. 2024

Nakladatel

ML Research Press

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

Proceedings of Machine Learning Research

Kód RIV

RIV/00216224:14330/24:00139577

Organizační jednotka

Fakulta informatiky

ISSN

EID Scopus

2-s2.0-85203794108

Klíčová slova anglicky

Machine learning; combinatorial optimization

Štítky

core_A, firank_1

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 11. 2024 09:30, RNDr. Vít Musil, Ph.D.

Anotace

V originále

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the embedded optimization problem often render the gradients uninformative. We propose Lagrangian Proximal Gradient Descent (LPGD), a flexible framework for training architectures with embedded optimization layers that seamlessly integrates into automatic differentiation libraries. LPGD efficiently computes meaningful replacements of the degenerate optimization layer derivatives by re-running the forward solver oracle on a perturbed input. LPGD captures various previously proposed methods as special cases, while fostering deep links to traditional optimization methods. We theoretically analyze our method and demonstrate on historical and synthetic data that LPGD converges faster than gradient descent even in a differentiable setup.

Návaznosti

GA23-06963S, projekt VaV

Název: VESCAA: Verifikovatelná a efektivní syntéza kontrolerů pro autonomní agenty

Investor: Grantová agentura ČR, VESCAA: Verifikovatelná a efektivní syntéza kontrolerů pro autonomní agenty

Citovat

PAULUS, Anselm; Georg MARTIUS a Vít MUSIL. LPGD: A General Framework for Backpropagation through Embedded Optimization Layers. Online. In Salakhutdinov R. and Kolter Z. and Heller K. and Weller A. and Oliver N. and Scarlett J. and Berkenkamp F. Proceedings of Machine Learning Research. 235. vyd. Neuveden: ML Research Press, 2024, s. 39989-40014. ISSN 2640-3498.

@inproceedings{2449779,
   author = {Paulus, Anselm and Martius, Georg and Musil, Vít},
   address = {Neuveden},
   booktitle = {Proceedings of Machine Learning Research},
   edition = {235},
   editor = {Salakhutdinov R. and Kolter Z. and Heller K. and Weller A. and Oliver N. and Scarlett J. and Berkenkamp F.},
   keywords = {Machine learning; combinatorial optimization},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Neuveden},
   pages = {39989-40014},
   publisher = {ML Research Press},
   title = {LPGD: A General Framework for Backpropagation through Embedded Optimization Layers},
   url = {https://proceedings.mlr.press/v235/paulus24a.html},
   year = {2024}
}

TY  - CONF
ID  - 2449779
AU  - Paulus, Anselm - Martius, Georg - Musil, Vít
PY  - 2024
TI  - LPGD: A General Framework for Backpropagation through Embedded Optimization Layers
PB  - ML Research Press
CY  - Neuveden
KW  - Machine learning
KW  - combinatorial optimization
UR  - https://proceedings.mlr.press/v235/paulus24a.html
N2  - Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the embedded optimization problem often render the gradients uninformative. We propose Lagrangian Proximal Gradient Descent (LPGD), a flexible framework for training architectures with embedded optimization layers that seamlessly integrates into automatic differentiation libraries. LPGD efficiently computes meaningful replacements of the degenerate optimization layer derivatives by re-running the forward solver oracle on a perturbed input. LPGD captures various previously proposed methods as special cases, while fostering deep links to traditional optimization methods. We theoretically analyze our method and demonstrate on historical and synthetic data that LPGD converges faster than gradient descent even in a differentiable setup.
ER  -

PAULUS, Anselm; Georg MARTIUS a Vít MUSIL. LPGD: A General Framework for Backpropagation through Embedded Optimization Layers. Online. In Salakhutdinov R. and Kolter Z. and Heller K. and Weller A. and Oliver N. and Scarlett J. and Berkenkamp F. \textit{Proceedings of Machine Learning Research}. 235. vyd. Neuveden: ML Research Press, 2024, s.~39989-40014. ISSN~2640-3498.

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