Research

Research Interests

My research interests can be roughly divided into two categories. One is about stochastic differential games and mean field games, together with related topics of applied probability, stochastic analysis, and partial differential equations. The other is machine learning, especially generative models, transfer learning and (inverse reinforcement) learning. A majority of the problems in the above areas arise from the fields of finance, economics and operations research and it is equally fascinating to see how the analytical and computational tools can help solve practical problems in these fields.

Publications and Preprints

Publications

• Haoyang Cao, Yuchao Dong and Zhouhao Yang. A Two-fold Randomization Framework for Impulse Control Problems. To appear in SIAM Journal on Control and Optimization, 2026.

• Haoyang Cao, Zhengqi Wu, and Renyuan Xu. Inference of Utilities and Time Preference in Sequential Decision-Making. Applied Mathematics and Optimization 92(3), pp. 1-49, 2025.

• Haoyang Cao, Xin Guo and Mathieu Lauriere. Connecting GANs, mean-field games and optimal transport. SIAM Journal on Applied Mathematics 84(4), pp. 1255-1287, 2024.

• Haoyang Cao and Xin Guo. SDE approximations of GANs training and its long-run behavior. Journal of Applied Probability 61(2), pp. 465-489, 2023.

• Haoyang Cao and Xin Guo. Generative Adversarial Networks: Some Analytical Perspective. Machine Learning for Financial Markets: a guide to contemporary practices, edited by Agostino Capponi and Charles-Albert Lehalle, Cambridge University Press, 2023.

• Haoyang Cao, Xin Guo and Joon Seok Lee. Approximation of N-player stochastic games with singular controls by mean field games. Numerical Algebra, Control and Optimization 13(3&4), pp. 604-629, 2023.

• Haoyang Cao, Jodi Dianetti, and Giorgio Ferrari. Stationary discounted and ergodic mean field games with singular controls. Mathematics of Operations Research 48(4), pp. 1871-1893, 2022.

• Matteo Basei, Haoyang Cao, and Xin Guo. Nonzero-sum stochastic games and mean-field games with impulse controls. Mathematics of Operations Research 47(1), pp. 341-366, 2022.

• Haoyang Cao and Xin Guo. MFGs for partially reversible investment. Stochastic Processes and their Applications, Vol. 150, pp. 995-1014, 2022.

• Haoyang Cao, Samuel N. Cohen and Lukasz Szpruch. Identifiability in inverse reinforcement learning. Advances in Neural Information Processing Systems 34, 2021.

Preprints

• Haoyang Cao, Xin Guo, Wenpin Tang and Guan Wang. Sample Complexity of Transfer Learning: An Optimal Transport Approach. Submitted, 2026.

• Haoyang Cao, Gokce Dayanikli, and Xiaofei Shi. Inverse Learning of the Altruism and Cost Level in Mixed-Individual Mean Field Games. Submitted, 2026.

• Haoyang Cao, Jesse Hoekstra, Renyuan Xu, Yumin Xu, and Ruixun Zhang. Scalable Bi-causal Optimal Transport via KL Relaxation and Policy Gradients. Preprint, 2026.

• Haoyang Cao, Minshuo Chen, Yinbin Han and Renyuan Xu. Diffusion Models for Adapted Sequential Data Generation (Journal Version). Preprint, 2026.

• Haoyang Cao, Minshuo Chen, Yinbin Han and Renyuan Xu. Diffusion Models for Adapted Sequential Data Generation (Short Version). NeurIPS 2025 Workshop MLxOR: Mathematical Foundations and Operational Integration of Machine Learning for Uncertainty-Aware Decision-Making, 2025.

• Haoyang Cao, Haotian Gu, Xin Guo, and Mathieu Rosenbaum. Risk of transfer learning and its applications in finance. In revision for Mathematical Finance, 2025.

• Haoyang Cao, Zhouhao Yang, and Vladimir Braverman. Generative model for Heavy-Tailed Distributions. Working paper, 2026.

• Haoyang Cao and Zhouhao Yang. Multi-agent system with randomized impulse control. Working paper, 2026.