arXiv:2511. 22331v2 Announce Type: replace-cross Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem.
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arXiv:2511. 19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure.
In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving th...
arXiv:2610.01662v1 Announce Type: cross Abstract: We establish complexity lower bounds for stochastic first-order algorithms in nonconvex--concave minimax optimization, allowing algorithms to use var...
arXiv:2606. 05438v1 Announce Type: new Abstract: We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions.
arXiv:2609. 30877v1 Announce Type: cross Abstract: We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization.
The paper investigates nonconvex–strongly-convex bilevel optimization using a stochastic first-order oracle. It introduces MRT‑FD, a single-loop first‑order algorithm that tracks the upper-level variable, the lower-level solution, and an auxiliary response from implicit differentiation, updating all variables in each iteration and approximating second‑order derivative actions via order‑p finite differences. For any fixed finite smoothness order p ≥ 1, MRT‑FD achieves an ε‑stationary point with O(ε^{‑4‑2/p}) stochastic gradient queries, and the authors prove a matching Ω(ε^{‑4‑2/p}) lower bound, thereby closing the complexity gap in this setting.