Huan-Jian Zhou

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...