Published in Journal of the American Statistical Association, 2026
Statistical inference for contextual bandits.
Recommended citation: Chen, Xi, Zehua Lai, He Li, and Yichen Zhang. "Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent." Journal of the American Statistical Association，(2026) http://laizehua.github.io/files/bandit.pdf
Published in arXiv, 2025
Pierce-Birkhoff conjecture is true for splines
Recommended citation: Zehua Lai, and Lek-Heng Lim. "Pierce-Birkhoff conjecture is true for splines." arXiv e-prints (2025): arXiv-2507.07976 https://arxiv.org/abs/2507.07976
Published in Optimization Letters, 2025
NP-hardness of linear optimization over Stiefel
Recommended citation: Zehua Lai, Lek-Heng Lim, and Tianyun Tang. "Stiefel optimization is NP-hard." Optimization Letters (to appear). https://arxiv.org/pdf/2507.02839
Published in SIAM Journal on Optimization, 2025
NP-hardness of quadratic optimization over Grassmannian
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Grassmannian optimization is NP-hard." SIAM Journal on Optimization, Volume 35, Issue 3, (2025) https://epubs.siam.org/doi/10.1137/24M1672596
Published in Foundations of Computational Mathematics, 2025
Compute differential geometry quantity in the Grassmannian.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simple matrix expressions for the curvatures of Grassmannian." Foundations of Computational Mathematics, (2025) https://link.springer.com/article/10. 1007/s10208-025-09723-9
Published in SIAM Journal on Optimization, 2025
Compute EDD of important manifolds.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Euclidean distance degree in manifold optimization." SIAM Journal on Optimization, Volume 35, Issue 4, (2025) https://epubs.siam.org/doi/full/10.1137/25M1735032
Published in arXiv, 2025
Splines are important in transformers.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Yucong Liu. "Attention is a smoothed cubic spline." arXiv e-prints (2024): arXiv-2408.09624 https://www.arxiv.org/pdf/2408.09624
Published in Computational Optimization and Applications, 2024
A stochastic generalization of Steffensen method.
Recommended citation: Minda Zhao, Zehua Lai, and Lek-Heng Lim. "Stochastic Steffensen Method." Computational Optimization and Applications, (2024) https://doi.org/10.1007/s10589-024-00583-7
Published in Journal of the American Statistical Association, 2023
Statistical inference in gradient free methods.
Recommended citation: Chen, Xi, Zehua Lai, He Li, and Yichen Zhang. "Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods." Journal of the American Statistical Association，(2023) https://doi.org/10.1080/01621459.2023.2296703
Published in arXiv, 2022
An extension of previous simpler Grassmannian optimization paper.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simpler Flag Optimization." arXiv e-prints (2021): arXiv-2212.00212 https://arxiv.org/pdf/2212.00212.pdf
Published in arXiv, 2022
A generalization of Haagerup method to Grothendieck Inequality for quaternions.
Recommended citation: Shmuel Friedland, Zehua Lai, and Lek-Heng Lim. "Haagerup Bound for Quaternionic Grothendieck Inequality." arXiv e-prints (2021): arXiv-2212.00208. https://arxiv.org/abs/2212.00208
Published in ICML, 2020
The noncommutative arithmetic-geometric mean inequality is false.
Recommended citation: Lai, Zehua, and Lek-Heng Lim. "Recht-Ré noncommutative arithmetic-geometric mean conjecture is false." In International Conference on Machine Learning, pp. 5608-5617. PMLR, 2020. http://proceedings.mlr.press/v119/lai20a/lai20a.pdf
Published in arXiv, 2020
A simpler model for optimization on Grassmannian manifolds. A follow-up paper deals with the flag manifolds.
Recommended citation: Lai, Zehua, Lek-Heng Lim, and Ke Ye. "Simpler Grassmannian optimization." arXiv e-prints (2020): arXiv-2009.13502 https://arxiv.org/pdf/2009.13502.pdf