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First-order penalty methods for bilevel optimization
March 8, 2024, 5:43 a.m. | Zhaosong Lu, Sanyou Mei
cs.LG updates on arXiv.org arxiv.org
Abstract: In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem. We introduce a notion of $\varepsilon$-KKT solution for them and show that an $\varepsilon$-KKT solution leads to an $O(\sqrt{\varepsilon})$- or $O(\varepsilon)$-hypergradient based stionary point under suitable assumptions. We also propose first-order penalty methods for finding an $\varepsilon$-KKT solution of …
abstract arxiv class cs.lg cs.na kkt math.na math.oc notion optimization paper show solution stat.ml study them type
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