Research

It is well recognized that the performance and convergence behavior of optimization algorithms depend critically on the underlying structure of the problem, such as convexity, error bounds, and subanalyticity. My research aims to identify and exploit the intrinsic structure of modern optimization problems, design algorithms that are tailored to these structures, and establish rigorous convergence guarantees. Beyond developing efficient algorithms, I am particularly interested in uncovering new principles, mechanisms, and analytical tools that deepen our understanding of optimization problems and the behavior of optimization methods.

Bilevel Optimization

Although numerous approximation algorithms have been developed for bilevel optimization under various notions of stationarity, relatively little is known about the relationships among these stationarity concepts, particularly their connection to hyper-stationarity. My research on bilevel optimization seeks to bridge this gap by establishing these connections and uncovering the structural properties of the hyper-objective function. I hope that these results can help clarify the theoretical foundations of existing approximation schemes and provide useful guidance for the design and analysis of optimization algorithms.

• Set Smoothness Unlocks Clarke Hyper-stationarity in Bilevel Optimization [arxiv]
  He Chen, Jiajin Li, Anthony Man-Cho So.
  The 39th Annual Conference on Neural Information Processing Systems (Neurips 2025, Spotlight)
• Lower-level Duality Based Reformulation and Majorization Minimization Algorithm for Hyperparameter Optimization
  He Chen, Haochen Xu, Rujun Jiang, Anthony Man-Cho So.
  The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024) [link]
• Fast Algorithms for Stackelberg Prediction Game with Least Squares Loss [link]
  Jiali Wang, He Chen, Rujun Jiang, Xudong Li, Zihao Li.
  The 38th International Conference on Machine Learning (ICML 2021)

Economic Computation

Classical algorithms for computing economic equilibria often rely on solving computationally expensive subproblems, which can become a bottleneck as market size and model complexity increase. My research on economic computation seeks to address this challenge by developing lightweight first-order methods that exploit the underlying optimization structure of these equilibrium problems. The goal is to design algorithms that are both computationally efficient and supported by rigorous theoretical guarantees.

• Accelerated Price Adjustment for Fisher Markets with Exact Recovery of Competitive Equilibrium [arxiv]
  He Chen, Chonghe Jiang, Anthony Man-Cho So ($\alpha$-$\beta$ order).
  The 21th Conference on Web and Internet Economics (WINE 2025)
• Computing Competitive Equilibrium for Chores: Linear Convergence and Lightweight Iteration [arxiv]
  He Chen, Chonghe Jiang, Anthony Man-Cho So.
  Revision at Games and Economic Behavior
  The 20th Conference on Web and Internet Economics (WINE 2024)