3 citations · 3 across the 1 of their papers we have counts for
7 papers
Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent
Xiangyu Chang, Xi Chen, Zehua Lai +3
With the fast development of big data, learning the optimal decision rule by recursively updating it and making online decisions has been easier than before. We study the online st…
Stiefel optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Tianyun Tang
We show that linearly constrained linear optimization over a Stiefel or Grassmann manifold is NP-hard in general. We show that the same is true for unconstrained quadratic optimiza…
Simple matrix expressions for the curvatures of Grassmannian
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q =…
Pierce-Birkhoff conjecture is true for splines
Zehua Lai, Lek-Heng Lim
We prove the Pierce--Birkhoff conjecture for splines, i.e., continuous piecewise polynomials of degree in variables on a hyperplane partition of , can be writ…
Euclidean distance degree in manifold optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we wi…
Grassmannian optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that unconstrained quadratic optimization over a Grassmannian is NP-hard. Our results cover all scenarios: (i) when and are both allowed to…