arXiv:2505. 02281v3 Announce Type: replace-cross Abstract: This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings.
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: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:2506.04192v4 Announce Type: replace-cross Abstract: Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers...
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:2609.30732v1 Announce Type: cross Abstract: We consider stochastic nonlinear optimization problems with deterministic equality constraints. While unconstrained stochastic optimization is well u...
arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv:2609.37425v1 Announce Type: cross Abstract: Fix a target accuracy $\varepsilon$, a gradient-noise level $s$, and a horizon $N$. We wish to design algorithms which minimize the probability of ob...
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
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:2504.09409v3 Announce Type: replace-cross Abstract: In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective e...
arXiv:2602. 01903v2 Announce Type: replace Abstract: This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime.