Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles

We study nonconvex--strongly-convex bilevel optimization with finite-sum objectives and fully first-order oracles. We propose Sampled Implicit Corrections for Bilevel Optimization (SICBO), which combines a penalty approximation with variance-reduced corrections for the lower-level variables. Under componentwise lower strong convexity, SICBO finds a point $x$ satisfying $\mathbb{E}\|\nablaΦ(x)\|^2\le\varepsilon^2$ within $\tilde{O}(N+\sqrt{N}κ^{7/2}\varepsilon^{-2})$ component-gradient calls, where $N$ is the total number of components and $κ$ is the normalized lower-level condition number. The bound achieves square-root finite-sum dependence using only gradients and preserves the best kno...

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