Lagrangian Duality for Constrained Deep Learning

Ferdinando Fioretto, Pascal Van Hentenryck, Terrence W.K. Mak, Cuong Tran, Federico Baldo, Michele Lombardi

Research output: Chapter in Book/Entry/PoemConference contribution

31 Scopus citations


This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning to predict solutions for constraint optimization problems which must be solved repeatedly and include hard physical and operational constraints. The paper also considers applications where the learning task must enforce constraints on the predictor itself, either because they are natural properties of the function to learn or because it is desirable from a societal standpoint to impose them. This paper demonstrates experimentally that Lagrangian duality brings significant benefits for these applications. In energy domains, the combination of Lagrangian duality and deep learning can be used to obtain state of the art results to predict optimal power flows, in energy systems, and optimal compressor settings, in gas networks. In transprecision computing, Lagrangian duality can complement deep learning to impose monotonicity constraints on the predictor without sacrificing accuracy. Finally, Lagrangian duality can be used to enforce fairness constraints on a predictor and obtain state-of-the-art results when minimizing disparate treatments.

Original languageEnglish (US)
Title of host publicationMachine Learning and Knowledge Discovery in Databases. Applied Data Science and Demo Track - European Conference, ECML PKDD 2020, Proceedings
EditorsYuxiao Dong, Dunja Mladenic, Craig Saunders
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783030676698
StatePublished - 2021
EventEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2020 - Virtual, Online
Duration: Sep 14 2020Sep 18 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12461 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2020
CityVirtual, Online

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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