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.
Constrained bi-level optimization: Proximal lagrangian value func- tion approach and hessian-free algorithm.arXiv preprint arXiv:2401.16164
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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.