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.
1, 32, arXiv:2309.024125
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Presents classical Õ(n²/ε^{1.5}) and quantum Õ(n/ε^{1.5}) query algorithms for ε-stationary points of twice-differentiable non-convex functions with Lipschitz gradient and Hessian via comparison oracles.
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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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Finding Stationary Points by Comparisons
Presents classical Õ(n²/ε^{1.5}) and quantum Õ(n/ε^{1.5}) query algorithms for ε-stationary points of twice-differentiable non-convex functions with Lipschitz gradient and Hessian via comparison oracles.