arXiv:2609. 23837v1 Announce Type: cross Abstract: We study the complexity of finding $(\delta,\epsilon)$-Goldstein stationary points of nonsmooth nonconvex Lipschitz functions.
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: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:2511. 13999v2 Announce Type: replace Abstract: We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses.
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.
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
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: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:2609.09524v1 Announce Type: cross Abstract: We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq \epsilon$, for a general norm $\|\cdot\|$ and a...
arXiv:2608. 09004v1 Announce Type: cross Abstract: We prove a sharp lower bound for smooth nonconvex stochastic optimization with uniformly bounded gradient noise.
We prove a sharp lower bound for smooth nonconvex stochastic optimization with uniformly bounded gradient noise. In the \(K=1\) fresh-sample model, every randomized adaptive algorithm requires $$Ω\left( \frac{ΔL}{ε^2} + \frac{ΔLσ^2}{ε^4} \right)$$ queries to find a point with expected gradient norm at most \(ε\).
arXiv:2609.24423v1 Announce Type: cross Abstract: We consider a standard convex composite optimization problem with either smooth or nonsmooth objective function, and under quadratic growth. In recen...