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.
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.
arXiv:2509. 14952v3 Announce Type: replace Abstract: This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex.
arXiv:2609. 06580v1 Announce Type: cross Abstract: We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives.
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: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.
The paper introduces single-loop stochastic projected damped extragradient (SPDE) and its variance-reduced variant (VR-SPDE) for stochastic nonconvex–(strongly) concave minimax problems. It provides SFO complexity bounds for achieving game stationarity and optimization stationarity, improving upon previous multi-loop methods while maintaining a single-loop structure. The results claim the best-known SFO complexities for these stationarity criteria among single-loop stochastic first‑order methods.
arXiv:2405. 00914v4 Announce Type: replace-cross Abstract: We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO).
arXiv:2609.30499v1 Announce Type: new Abstract: Uniform noise-moment bounds exclude stochastic gradients whose variability increases with the iterate. We study ordinary, single-sample stochastic grad...
arXiv:2609.08380v1 Announce Type: cross Abstract: We study the stochastic first-order oracle complexity for constrained or regularized convex-concave min-max optimization and stochastic monotone vari...
arXiv:2609. 30501v1 Announce Type: new Abstract: Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.
arXiv:2512. 02494v2 Announce Type: replace Abstract: Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems.
arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.