Currently, I am an Assistant Professor at Department of Industrial Engineering and Operations Research, Columbia University. Before joining Columbia IEOR, I was a postdoctoral researcher at Department of Industrial Engineering and Operations Research, UC Berkeley, and an assistant adjunct professor at Department of Mathematics, UCLA. I obtained my Ph.D. from Department of Statistics, UC Berkeley. My advisor was Jim Pitman . Before coming to Berkeley, I obtained an engineer diploma (Diplôme d'ingénieur) from Ecole Polytechnique, France.
My research interests are probability theory, machine learning, and financial technology. I am currently working on classifier guidance of diffusion models from a stochastic analysis perspective.
[54] The soccer model, stochastic ordering and martingale transport .
with Gaoyue Guo and Nicolas Juillet. Submitted.
[53] Fine-tuning diffusion generative models via rich preference optimization .
with Hanyang Zhao, Haoxian Chen, Yucheng Guo, Tingting Ou, Ziyu Huang, Genta Indra Winata and David Yao. Submitted.
[52] Analysis of the order flow auction under proposer-builder separation.
with Ruofei Ma and David Yao. Submitted.
[51] Regret of exploratory policy improvement and q-learning .
with Xun Yu Zhou. Submitted.
[50] Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond .
Submitted.
[49] Score-based diffusion models via stochastic differential equations -- a technical tutorial .
with Hanyang Zhao. Submitted (growing out of the writeup).
[48] Contractive diffusion probabilistic models .
with Hanyang Zhao. Submitted. .
[47] Transaction fee mechanism for Proof-of-Stake protocol .
with David D. Yao. Submitted.
[46] Finite and infinite weighted exchangeable sequences .
Submitted.
[45] Exact Bayesian geostatistics using predictive stacking .
with Lu Zhang and Sudipto Banerjee. Submitted.
[44] Stability of shares in the Proof of Stake protocol -- concentration and phase transitions .
Submitted.
[43] Learning an arbitrary mixture of two multinomial logits
.
Submitted.
[42] Score as action: fine-tuning diffusion generative models by continuous-time reinforcement learning .
with Hanyang Zhao, Haoxian Chen, Ji Zhang and David D. Yao. To appear in International Conference on Machine Learning (ICML 2025) (growing out of the position paper ). A preliminary version in DeLTa Workshop @ ICLR 2025 .
[41] The convergence rate of vanishing viscosity approximations for mean field games .
with Yuming Paul Zhang. To appear in SIAM Journal on Mathematical Analysis .
[40] Preference tuning with human feedback on language, speech, and vision tasks: a survey .
with Genta Indra Winata, Hanyang Zhao, Anirban Das, David D. Yao, Shi-Xiong Zhang and Sambit Sahu. Journal of Artificial Intelligence Research (2025) vol.82, 2595-2661 .
[39] RainbowPO: a unified framework for combining improvements in preference optimization .
with Hanyang Zhao, Genta Indra Winata, Anirban Das, Shi-Xiong Zhang, David D. Yao and Sambit Sahu. International Conference on Learning Representation (ICLR 2025) .
[38] MallowsPO: fine-tune your LLM with preference dispersions .
with Haoxian Chen, Hanyang Zhao, Henry Lam and David Yao. International Conference on Learning Representation (ICLR 2025) . A preliminary version in Pluralistic Alignment Workshop @ NeurIPS 2024 .
[37] Systemic robustness: a mean-field particle system approach .
with Erhan Bayraktar, Gaoyue Guo and Yuming Paul Zhang. To appear in Mathematical Finance .
[36] Policy iteration for the deterministic control problems -- a viscosity approach .
with Hung Vinh Tran and Yuming Paul Zhang. SIAM Journal on Control and Optimization (2025) vol.63, no.1, 375-401 .
[35] Discrete simulated annealing: a convergence analysis via the Eyring--Kramers law .
with Yuhang Wu and Xun Yu Zhou. Numerical Algebra, Control and Optimization (2024) vol.14, no.4, 778-794 .
[34] Polynomial voting rules .
with David D. Yao. Mathematics of Operations Research (2025) vol.50, no.1, 90-106.
[33] Trading and wealth evolution in the Proof of Stake protocol .
Proof-of-Stake for Blockchain Networks: Fundamentals, Challenges and Approaches (2024) Chapter 7, 135-161.
[32] Fixed-domain asymptotics under Vecchia's approximation of spatial process likelihoods .
with Lu Zhang and Sudipto Banerjee. Statistica Sinica (2024) vol.34, no.4, 1863-1881.
[31] McKean-Vlasov equations involving hitting times: blow-ups and global solvability
.
with Erhan Bayraktar, Gaoyue Guo and Yuming Paul Zhang. Annals of Applied Probability (2024) vol.34, no.1B, 1600–1622.
[30] Escaping saddle points efficiently with occupation-time-adapted perturbations .
with Xin Guo, Jiequn Han and Mahan Tajrobehkar. Journal of Computational Mathematics and Data Science (2024) vol.10, 100090.
[29] Policy optimization for continuous reinforcement learning .
with David D. Yao and Hanyang Zhao. Advances in Neural Information Processing Systems (Neurips 2023) vol.36, 13637-13663.
[28] One-dependent hard-core processes and colorings of the star graph .
with Thomas Liggett. Annals of Applied Probability (2023) vol.33, no.6A, 4341–4365.
[27] Trading under the Proof-of-Stake protocol -- a continuous-time control approach .
with David D. Yao. Mathematical Finance (2023) vol.33, no.4, 979-1004.
[26] Tail probability estimates of continuous-time simulated annealing processes .
with Xun Yu Zhou. Numerical Algebra, Control and Optimization (2023) vol.13, no.3-4, 473-485.
[25] Fixed-domain inference for Gausian processes with Matérn covariogram on compact Riemannian manifolds .
with Didong Li and Sudipto Banerjee. Journal of Machine Learning Research (2023) vol.24, no.101, 1-26.
[24] Extreme order statistics of random walks
.
with Jim Pitman. Annales de l'Institut Henri Poincaré (2023) vol.59, no.1, 97-116.
[23] The Poisson binomial distribution -- Old & New .
with Fengmin Tang. Statistical Science (2023) vol.38, no.1, 108-119.
[22] Exploratory HJB equations and their convergence .
with Yuming Zhang and Xun Yu Zhou. SIAM Journal on Control and Optimization (2022) vol.60, no.6, 3191-3216.
[21] Ergodicity of the infinite swapping algorithm at low temperature .
with Georg Menz, André Schlichting and Tianqi Wu. Stochastic Processes and their Applications (2022) vol 151, 519-552.
[20] Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walk .
with Jim Pitman. Annals of Probability (2022) vol.50, no.4, 1647-1673.
[19] Parallel search for information in continuous time -- optimal stopping and geometry of the PDE .
with T. Tony Ke, J. Miguel Villas-Boas and Yuming Zhang. Applied Mathematics and Optimization (2022) vol.85, article 3, 1-25.
[18] Asset selection via correlation blockmodel clustering .
with Xiao Xu and Xun Yu Zhou. Expert Systems with Applications (2022) vol.195, 116558.
[17] A stochastic game and stochastic free boundary problem .
with Xin Guo and Renyuan Xu. SIAM Journal on Control and Optimization (2022) vol.60, no.2, 758-785.
[16] On identifiability and consistency of the nugget in Gaussian spatial process models .
with Lu Zhang and Sudipto Banerjee. Journal of the Royal Statistical Society: Series B (2021) vol.83, no.5, 1044-1070.
[15] Arcsine laws for random walks generated from random permutations with applications to genomics .
with Xiao Fang, Han Liang Gan, Susan Holmes, Haiyan Huang, Erol Peköz and Adrian Röllin. Journal of Applied Probability (2021) vol.58, no.4, 851-867.
[14] The existence of maximum likelihood estimate in high-dimensional generalized linear models with binary responses .
with Yuting Ye. Electron. J. Statist (2020) vol.14, no.2, 4028-4053.
[13] The Buckley-Osthus model and the block preferential attachment model: statistical analysis and application .
with Xin Guo and Fengmin Tang. Proceedings of the 37th International Conference on Machine Learning (ICML 2020) PMLR 119, 9377-9386.
[12] Mallows ranking models: maximum likelihood estimate and regeneration .
Proceedings of the 36th International Conference on Machine Learning (ICML 2019) PMLR 97, 6125-6134.
[11]
Exponential ergodicity and convergence for generalized reflected Brownian motion .
Queueing Systems: Theory and Applications (2019) vol.92, no.1, 83-101.
[10] Renewal sequences and record chains related to multiple zeta sums .
with Jean-Jil Duchamps and Jim Pitman. Transactions of AMS (2019) vol.371, no.8, 5731-5755.
[9] Regenerative random permutations of integers .
with Jim Pitman. Annals of Probability (2019) vol.47, no.3, 1378-1416.
[8] Transporting random measures on the line and embedding excursions into Brownian motion .
with Günter Last and Hermann Thorisson. Annales de l'Institut Henri Poincaré (2018) vol.54, no.4, 2286-2303.
[7] The argmin process of random walks, Brownian motion and Lévy processes .
with Jim Pitman. Electro. J. Probab (2018) vol.23, no.60, 1-35.
[6] Optimal surviving strategy for drifted Brownian motions with absorption .
with Li-Cheng Tsai. Annals of Probability (2018) vol.46, no.3, 1597-1650.
[5] Tree formulas, mean first passage times and Kemeny's constant of a Markov chain .
with Jim Pitman. Bernoulli (2018) vol.24, no.3, 1942-1972.
[4] The spans in Brownian motion .
with Steve Evans and Jim Pitman. Annales de l'Institut Henri Poincaré (2017) vol.53, no.3, 1108-1135.
[3] The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift .
with Jim Pitman. Electro. J. Probab (2015) vol.20, no.61, 1-28.
[2] Patterns in random walks and Brownian motion .
with Jim Pitman. Séminaire de probabilité XLVII - In Memoriam Marc Yor (2015), 49-88.
[1] The Vervaat transform of Brownian bridges and Brownian motion .
with Titus Lupu, Jim Pitman. Electro. J. Probab (2015) vol.20, no.51, 1-31.
In Fall 2021, I will teach IEOR E4706: Foundations of Financial Engineering.