Second-order bilevel methods achieve Õ(ε^{-1.5}) iteration complexity for second-order stationary points, faster than first-order approaches, with a lazy variant improving computational efficiency by √d.
A primal-dual ap- proach to bilevel optimization with multiple inner minima
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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.
Bilevel learning methods rely on implicit differentiation but are restricted by assumptions of unique lower-level solutions and struggle with constraints, and connections to broader bilevel optimization literature may enable more scalable general-purpose algorithms.
citing papers explorer
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Second-Order Bilevel Optimization with Accelerated Convergence Rates
Second-order bilevel methods achieve Õ(ε^{-1.5}) iteration complexity for second-order stationary points, faster than first-order approaches, with a lazy variant improving computational efficiency by √d.
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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.
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Bilevel learning
Bilevel learning methods rely on implicit differentiation but are restricted by assumptions of unique lower-level solutions and struggle with constraints, and connections to broader bilevel optimization literature may enable more scalable general-purpose algorithms.