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- Title
Stochastic inexact augmented Lagrangian method for nonconvex expectation constrained optimization.
- Authors
Li, Zichong; Chen, Pin-Yu; Liu, Sijia; Lu, Songtao; Xu, Yangyang
- 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 ε -KKT point in expectation, we establish an oracle complexity result of O (ε - 5) , which is better than the best-known 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.
- Subjects
PROBLEM solving; CONSTRAINED optimization; FAIRNESS; NONSMOOTH optimization
- Publication
Computational Optimization & Applications, 2024, Vol 87, Issue 1, p117
- ISSN
0926-6003
- Publication type
Article
- DOI
10.1007/s10589-023-00521-z