Stochastic inexact augmented Lagrangian method for nonconvex expectation constrained optimization

Zichong Li (), Pin-Yu Chen (), Sijia Liu (), Songtao Lu () and Yangyang Xu ()
Additional contact information
Zichong Li: Rensselaer Polytechnic Institute
Pin-Yu Chen: Thomas J. Watson Research Center
Sijia Liu: Michigan State University
Songtao Lu: Thomas J. Watson Research Center
Yangyang Xu: Rensselaer Polytechnic Institute

Computational Optimization and Applications, 2024, vol. 87, issue 1, No 4, 117-147

Abstract: Abstract Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In this paper, we design and analyze stochastic inexact augmented Lagrangian methods (Stoc-iALM) to solve problems involving a nonconvex composite (i.e. smooth + nonsmooth) objective and nonconvex smooth functional constraints. We adopt the standard iALM framework and design a subroutine by using the momentum-based variance-reduced proximal stochastic gradient method (PStorm) and a postprocessing step. Under certain regularity conditions (assumed also in existing works), to reach an $$\varepsilon $$ ε -KKT point in expectation, we establish an oracle complexity result of $$O(\varepsilon ^{-5})$$ O ( ε - 5 ) , which is better than the best-known $$O(\varepsilon ^{-6})$$ O ( ε - 6 ) result. Numerical experiments on the fairness constrained problem and the Neyman–Pearson classification problem with real data demonstrate that our proposed method outperforms an existing method with the previously best-known complexity result.

Keywords: First-order methods; Expectation constraint; Augmented Lagrangian; Nonconvex optimization; Momentum acceleration (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-023-00521-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:87:y:2024:i:1:d:10.1007_s10589-023-00521-z

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-023-00521-z

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().