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.
Prox-method with rate of convergence o(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems
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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.