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. 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: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:2608. 09004v1 Announce Type: cross Abstract: We prove a sharp lower bound for smooth nonconvex stochastic optimization with uniformly bounded gradient noise.
arXiv:2503. 04712v3 Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods.
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.
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:2608. 10418v1 Announce Type: cross Abstract: Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications.
arXiv:2510. 01943v3 Announce Type: replace-cross Abstract: Quasar-convex functions form a broad nonconvex class with applications to linear dynamical systems, generalized linear models, and Riemannian optimization, among others.
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
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:2606. 01764v1 Announce Type: cross Abstract: We revisit the convergence guarantees of the Extragradient (EG) method for unconstrained biaffine min-max optimization.