Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
arXiv preprint arXiv:2309.01753 , year=
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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.
Formalizes Root-Finding Bilevel Optimization (RF-BO) and introduces a Jacobian-free TTSA algorithm that structurally avoids variance amplification, with convergence guarantees and reported gains over squared-residual baselines in SimCLR, ODE control, RL entropy tuning, and generative modeling.
BROS achieves memory-efficient single-loop stochastic bilevel optimization with O(ε^{-2}) sample complexity by performing updates in randomized subspaces and using Rademacher bi-probe correction for unbiased estimation.
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Escaping the Variance Trap: Jacobian-Free Dynamics for Root-Finding Bilevel Optimization
Formalizes Root-Finding Bilevel Optimization (RF-BO) and introduces a Jacobian-free TTSA algorithm that structurally avoids variance amplification, with convergence guarantees and reported gains over squared-residual baselines in SimCLR, ODE control, RL entropy tuning, and generative modeling.
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BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization
BROS achieves memory-efficient single-loop stochastic bilevel optimization with O(ε^{-2}) sample complexity by performing updates in randomized subspaces and using Rademacher bi-probe correction for unbiased estimation.