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.
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.
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...
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:2609. 17973v1 Announce Type: cross Abstract: We introduce a new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization.
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: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:2607. 08954v1 Announce Type: cross Abstract: We study nonasymptotic convergence of primal-dual methods for a class of nonconvex constrained optimization problems with a convex-composite structure.
arXiv:2609.06064v1 Announce Type: cross Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...
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.