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, 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, Zhengqi Wu, and Renyuan Xu. Inference of Utilities and Time Preference in Sequential Decision-Making. Submitted, 2024.

• Haoyang Cao, Haotian Gu, Xin Guo. Feasibility and risk of transfer learning: a mathematical framework. Working paper, 2024.

• Haoyang Cao, Xin Guo and Guan Wang. Meta-learning with GANs for anomaly detection, with deployment in high-speed rail inspection system. Working paper, 2024.

• Guan Wang, Yusuke Kikuchi, Haoyang Cao, Jinglin Yi, Qiong Zou, Rui Zhou, and Xin Guo. Transfer learning for retinal vascular disease detection: a pilot study with diabetic retinopathy and retinopathy of prematurity. Working paper, 2024.

• Haoyang Cao, Haotian Gu, Xin Guo, and Mathieu Rosenbaum. Risk of transfer learning and its applications in finance. Submited, 2023.

• Qinkai Chen, Mohamed El-Mennaoui, Antoine Fosset, Amine Rebei, Haoyang Cao, Philine Bouscasse, Christy Eóin O’Beirne, Sasha Shevchenko, and Mathieu Rosenbaum. Towards mapping the contemporary art world with ArtLM: an art-specific NLP model. Submitted, 2023.