Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
arXiv preprint arXiv:2406.06874 , year=
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Penalty-based first-order methods find ε-KKT points in bilevel minimax problems with Õ(ε^{-4}) deterministic and Õ(ε^{-9}) stochastic oracle complexity, improving prior bounds for constrained lower-level cases via Lagrangian duality.
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On the Nature of Regularity Assumptions in Bilevel Optimization with Constrained Lower-level Problem
Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
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Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems
Penalty-based first-order methods find ε-KKT points in bilevel minimax problems with Õ(ε^{-4}) deterministic and Õ(ε^{-9}) stochastic oracle complexity, improving prior bounds for constrained lower-level cases via Lagrangian duality.