Lagrangian Duality for Constrained Deep Learning

By Ferdinando Fioretto, Pascal Van Hentenryck, Terrence W.K. Mak, Cuong Tran, Federico Baldo, Michele Lombardi. 2020

111 citations recorded by the source corpus.

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 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.

Subfields: Artificial Intelligence, Computer Networks and Communications, Ocean Engineering, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Simon Lacoste-Julien
2. Yoshua Bengio
3. Peter Richtárik
4. Martin Jaggi
5. Pascal Vincent
6. Michael I. Jordan
7. Francis R. Bach
8. Kyunghyun Cho

In Computer Networks and Communications

1. Simon Lacoste-Julien
2. Jose Gallego-Posada
3. Yoshua Bengio

In Ocean Engineering

1. Simon Lacoste-Julien
2. Yoshua Bengio

In Optimization & Training

1. Simon Lacoste-Julien
2. Yoshua Bengio
3. Jose Gallego-Posada
4. Juan Ramirez
5. Akram Erraqabi
6. Fabian Pedregosa
7. Peter Richtárik
8. Pascal Vincent

Citations in the corpus

• Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints (2022, background): “Fioretto et al. [10] consider a wide range of applications spanning from optimal power flow in energy grids, to the training of fair classification models.”