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.
Efficient first or- der method for saddle point problems with higher or- der smoothness.SIAM Journal on Optimization, 34(4): 3342–3370, 2024a
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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.