Backpropagation of Unrolled Solvers with Folded Optimization

James Kotary, My H. Dinh, Ferdinando Fioretto

Research output: Chapter in Book/Entry/PoemConference contribution


The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which typically lacks a closed form. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. While flexible and general, unrolling can encounter accuracy and efficiency issues in practice. These issues can be avoided by analytical differentiation of the optimization, but current frameworks impose rigid requirements on the optimization problem's form. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation. Additionally, it proposes a unifying view of unrolling and analytical differentiation through optimization mappings. Experiments over various model-based learning tasks demonstrate the advantages of the approach both computationally and in terms of enhanced expressiveness.

Original languageEnglish (US)
Title of host publicationProceedings of the 32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
EditorsEdith Elkind
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages8
ISBN (Electronic)9781956792034
StatePublished - 2023
Externally publishedYes
Event32nd International Joint Conference on Artificial Intelligence, IJCAI 2023 - Macao, China
Duration: Aug 19 2023Aug 25 2023

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Conference32nd International Joint Conference on Artificial Intelligence, IJCAI 2023

ASJC Scopus subject areas

  • Artificial Intelligence


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