Research

I have broad interests in modern optimization theory, with a particular focus on game-structure optimization. In my representative work ⭐, I have collaborated with my excellent coauthors to solve many fundamental problems in this area, such as the oracle complexity of convex, nonconvex, minimax, and bilevel optimization.

Research Highlights

1. Second-Order Minimax Optimization [Slides in SIAM OP 26] [Expand]
   Upper Bound: $\tilde{\mathcal{O}}(1/T^{1.75})$ [COLT 2025] $\to$ $\tilde{\mathcal{O}}(1/T^{2})$ [arXiv 2026]
   Lower Bound: $\Omega(1/T^{2.5})$ [arXiv 2026]
   
2. Bilevel Optimization [Slides in SIAM OP 26] [Expand]
   Upper Bound: $\tilde{\mathcal{O}}(\kappa^{3.5} \epsilon^{-2} + \sigma^2 \kappa^{11} \epsilon^{-6})$ [JMLR 2025]
   Lower Bound: $\Omega(\kappa^{2.5} \epsilon^{-2} + \sigma^2 \kappa^{4.5} \epsilon^{-4})$ [arXiv 2025]
   

Working Papers

1. Lesi Chen¹, Xinliang Zhang ¹, Junru Li, Chengchang Liu, Luo Luo, and Jingzhao Zhang, Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/(3p+1)})$ pth-Order Oracle Complexity, arXiv preprint. [arXiv 2026]
   Preliminary version in Conference on Learning Theory. (Best Student Paper, 2/556) [COLT 2025] ⭐

2. Lesi Chen¹ , Kaiyi Ji ¹, and Jingzhao Zhang, On the Condition Number Dependency in Bilevel Optimization, arXiv preprint. [arXiv 2025] ⭐

3. Lesi Chen, Chengchang Liu, Luo Luo, John C.S. Lui, and Jingzhao Zhang, Optimal Convex Optimization with Inexact Second-Order Oracles , arXiv preprint. [arXiv 2026]

Featured Publications

1. Lesi Chen, Chengchang Liu, Luo Luo, and Jingzhao Zhang, Faster Newton Methods for Convex and Nonconvex Optimization in Gradient Complexity , in Conference on Learning Theory. [COLT 2026] ⭐

2. Lesi Chen, Junru Li, El Mahdi Chayti and Jingzhao Zhang, Faster Gradient Methods for Highly-Smooth Stochastic Bilevel Optimization, in International Conference on Learning Representations. [ICLR 2026]

3. Lesi Chen¹, Yaohua Ma¹, and Jingzhao Zhang, Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles , Journal of Machine Learning Research, 1-56. [JMLR 2025] ⭐
   

4. Lesi Chen¹, Chengchang Liu¹, and Jingzhao Zhang, Second-Order Min-Max Optimization with Lazy Hessians, in International Conference on Learning Representations. (Oral, <2%) [ICLR 2025]

5. Lesi Chen and Luo Luo, Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization, Journal of Machine Learning Research, 1-44. [JMLR 2024]

6. Huaqing Zhang¹, Lesi Chen¹, Jing Xu, and Jingzhao Zhang, Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems, in Conference on Neural Information Processing Systems.
   [NeurIPS 2024]

7. Lesi Chen¹, Jing Xu¹, and Jingzhao Zhang, On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysis, in Conference on Learning Theory. [COLT 2024]

8. Lesi Chen, Jing Xu, and Luo Luo, Faster Gradient-Free Algorithms for Nonsmooth Nonconvex Stochastic Optimization, in International Conference on Machine Learning. [ICML 2023]

9. Lesi Chen, Boyuan Yao, and Luo Luo, Faster Stochastic Algorithms for Minimax Optimization under Polyak-Łojasiewicz Condition, in Conference on Neural Information Processing Systems. [NeurIPS 2022]

See Google Scholar for a complete list.