arXiv:2608. 09004v1 Announce Type: cross Abstract: We prove a sharp lower bound for smooth nonconvex stochastic optimization with uniformly bounded gradient noise.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
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: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:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
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:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.