Author

Huan-Jian Zhou

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Preprint Oct 2026

On Complexity of Gaussian Sampling

We study the number of exact matrix-vector queries needed to sample a centered $d$-dimensional Gaussian with condition number at most $\kappa$ to total variation error $\varepsilon$. The best known algorithm uses $O(\min\{d,\sqrt{\kappa}\log(\frac{d}{\varepsilon})\})$ queries, while the known lower bounds do not grow a...

Huan-Jian Zhou, Taiji Suzuki · 0 citations

Preprint Oct 2026

Finding Stationary Points under Higher-Order Smoothness: Trapping Algorithms and First-Order Lower Bounds

We study the query complexity of finding approximate stationary points under higher-order smoothness using only function values or only gradients. Our results cover different dimensions, oracle models, randomization, and constraints. For constant dimension $d$ and $C^{p,\beta_p}$ objectives, with $\nu:=p+\beta_p$, we g...

Huan-Jian Zhou, Masashi Sugiyama, Taiji Suzuki · 2 citations · ⚡1