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.

[51] Regret of exploratory policy improvement and q-learning .

with Xun Yu Zhou.

[50] 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. Submitted.

[49] 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. Submitted.

[48] Scores as Actions: a framework of fine-tuning diffusion models by continuous-time reinforcement learning .

with Haoxian Chen, Hanyang Zhao, Ji Zhang and David Yao.

[47] MallowsPO: fine-tune your LLM with preference dispersions .

with Haoxian Chen, Hanyang Zhao, Henry Lam and David Yao. Submitted.

[46] Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond .

Submitted.

[45] Score-based diffusion models via stochastic differential equations -- a technical tutorial .

with Hanyang Zhao. Submitted (growing out of the writeup).

[44] Contractive diffusion probabilistic models .

with Hanyang Zhao. Submitted. .

[43] Transaction fee mechanism for Proof-of-Stake protocol .

with David D. Yao. Submitted.

[42] Finite and infinite weighted exchangeable sequences .

Submitted.

[41] Exact Bayesian geostatistics using predictive stacking .

with Lu Zhang and Sudipto Banerjee. Submitted.

[40] The convergence rate of vanishing viscosity approximations for mean field games .

with Yuming Paul Zhang. Submitted.

[39] Systemic robustness: a mean-field particle system approach .

with Erhan Bayraktar, Gaoyue Guo and Yuming Paul Zhang. Submitted.

[38] Stability of shares in the Proof of Stake protocol -- concentration and phase transitions .

Submitted.

[37] Learning an arbitrary mixture of two multinomial logits
.

Submitted.

[36] Policy iteration for the deterministic control problems -- a viscosity approach .

with Hung Vinh Tran and Yuming Paul Zhang. To appear in * SIAM Journal on Control and Optimization *.

[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. To appear in * Mathematics of Operations Research. *

[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. To appear in * Statistica Sinica. *

[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. *

August, 2024: Oregon, Joint Statistical Meetings .

July, 2024: Rio de Janeiro, 12th Bachelier World Congress .

April, 2024: Rice Univeristy, CMOR Colloquium .

Jan, 2024: University of Texas at San Antonio, ECE seminar .

Oct, 2023: Pheonix, INFORMS .

Sept, 2023: Virtual, CityU-NUS Mean Field Game and Control Seminar .

Sept, 2023: University of Pennsylvania, Wharton Statistics seminar .

July, 2023: Lisbon, 43rd Conference on Stochastic Processes and their Applications .

May, 2023: Carnegie Mellon University, Secure Blockchain Summit .

Mar, 2023: University of Pennsylvania, Penn/Temple Probability Seminar .

Feb, 2023: Columbia University, Applied Mathematics Colloquium .

Nov, 2022: Virtual, Hong Kong-Singapore joint seminar in Financial Mathematics/Engineering .

Nov, 2022: Columbia University, Mathematical Finance seminar .

Oct, 2022: Indianapolis, INFORMS .

July, 2022: SIAM Annual Meeting, Machine Learning in Finance: Theory and Application .

May, 2022: Institute for Mathematical and Statistical Innovation, Workshop: Machine Learning and Mean Field Games .

Feb, 2022: University of Southern California, Mathematical Finance Colloquium .

Nov, 2021: Princeton University, ORFE Financial Mathematics seminar .

Oct, 2021: UCLA, Probability seminar .

July, 2021: Institute for Mathematical and Statistical Innovation, Program: Introduction to Decision Making and Uncertainty .

June, 2021: Paris, Séminaire Bachelier .

May, 2021: University of Mannheim, Probability seminar .

Dec, 2020: Virtual, Workshop on Optimization, Probability, and Simulation.

Oct, 2020: Virtual, INFORMS .

Mar, 2020: University of Michigan, Financial/Actuarial Mathematics Seminar .

Feb, 2020: Cornell University, ORIE Colloqium .

Feb, 2020: Columbia University, IEOR Department Seminar .

Jan, 2020: Baruch College, Mathematics Colloquium .

Jan, 2020: University of Utah, Mathematics Colloqium .

Jan, 2020: Northwestern University, Mathematics Colloqium .

Dec, 2019: University of Cincinnati, Probability Seminar .

Dec, 2019: University of Miami, Mathematics Colloquium .

Nov, 2019: North Carolina State University, Mathematics Colloquium .

Nov, 2019: Riverside, AMS meeting .

Nov, 2019: UCSD, Probability Seminar .

Oct, 2019: University of Washington, Probability Seminar .

Oct, 2019: Seattle, INFORMS .

Sept, 2019: UC Berkeley, Probabilty Seminar .

June, 2019: Los Angeles, ICML Oral .

Feb, 2019: UCLA, Combinatorics Seminar .

Dec, 2018: Los Angeles, Southern California Probability Symposium .

Oct, 2018: San Francisco, AMS meeting .

July, 2018: Stanford, Workshop in memory of Larry Shepp .

Feb, 2018: Stanford University, Probability Seminar .

Feb, 2018: UC Berkeley, IEOR Colloquium .

Dec, 2017: University of Chicago, Probability and Statistical physics seminar .

Nov, 2017: UCLA, Probability Seminar .

Mar, 2017: UCLA, Probability Seminar .

Mar, 2017: UC Berkeley, Probability Seminar .

July, 2016: Edmonton, IMS-FIPS Workshop .

Mar, 2016: Berkeley, Berkeley-Columbia Meeting in Engineering and Statistics .

Feb, 2015: UC Davis, Mathematical Physics and Probability Seminar .

Feb, 2015: UC Berkeley, Probability Seminar .

Oct, 2014: UC Berkeley, Student Probability/PDE Seminar .

July, 2014: Saint-Flour, 44th probability summer school.

June, 2014: San Diego, Combinatorial Stochastic Processes: A conference in celebration of Jim Pitman's 65th birthday .

July, 2013: Saint-Flour, 43rd probability summer school.

Sept, 2013: UC Berkeley, SGSA Student Seminar .

In Fall 2021, I will teach IEOR E4706: Foundations of Financial Engineering.