AN IMPLICIT GRADIENT-TYPE METHOD FOR LINEARLY CONSTRAINED BILEVEL PROBLEMS

Ioannis Tsaknakis, Prashant Khanduri, Mingyi Hong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work, we develop an implicit gradient-type (IG-AL) algorithm for bilevel optimization with strongly convex linear inequality constrained lower-level problems. Many learning problems of interest, including problems in distributed optimization, machine learning, economics, and transport research are captured by the above formulation. The key characteristics of the proposed algorithm are: (i) the use of a primal-dual augmented Lagrangian method for solving the lower-level problem, and (ii) construction of an implicit gradient (derived using the KKT conditions of the lower-level problem) for solving the upper-level problem. Importantly, the proposed algorithm avoids the (expensive) projection step to a half-space inherent to gradient descent-based alternatives. The performance of the proposed algorithm is evaluated on a set of numerical experiments.

Original languageEnglish (US)
Title of host publication2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5438-5442
Number of pages5
ISBN (Electronic)9781665405409
DOIs
StatePublished - 2022
Event47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Virtual, Online, Singapore
Duration: May 23 2022May 27 2022

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2022-May
ISSN (Print)1520-6149

Conference

Conference47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022
Country/TerritorySingapore
CityVirtual, Online
Period5/23/225/27/22

Bibliographical note

Publisher Copyright:
© 2022 IEEE

Keywords

  • constrained bilevel optimization
  • implicit gradient

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