Liyuan Distinguished Scholars Lecture Series No. 36: Solving Hamilton-Jacobi-Bellman Equations using at most four-armed slot machines

Shenzhen University School of Mathematical Sciences  

Liyuan Distinguished Scholars Lecture Series No. 36  

Lecture Title: Solving Hamilton-Jacobi-Bellman Equations using at most four-armed slot machines

Speaker: Chen Zengjing (Professor, Shandong University)  

Date & Time: 10:00–11:00 AM, April 29, 2025  

Venue: Classroom 1, Huixing Building, Yuehai Campus, Shenzhen University  

Abstract: Formulating algorithms to solve constrained high-dimensional Hamilton-Jacobi-Bellman equations has long been challenging, largely due to the inherent complexities associated with the constrained condition and the “curse of dimensionality”. Artificial Intelligence (AI), by mimicking human cognition, has significantly advanced the resolution of open problems across various fields, as exemplified by the “cap set problem” with “FunSearch”. This work pioneers a novel AI-based approach by transforming the challenge of solving general constrained high-dimensional Hamilton-Jacobi-Bellman equations into a problem of optimizing strategies with multiple four-armed slot machines. This approach leverages an equivalence between certain stochastic control problems and the multi-armed slot machine framework, recasting finite-region control as a policy optimization challenge over an infinite strategy set. It represents a groundbreaking application of AI methodologies to a classical class of partial differential equations, with promising potential for broad applications in fields such as finance, engineering, and physics.

Biography: Chen Zengjing is a professor at the School of Mathematics, Shandong University, and the Dean of the Zhongtai Securities Institute of Financial Studies, Shandong University. His main research areas include financial mathematics, backward stochastic differential equations, nonlinear expectations, and econometrics. He has received several prestigious awards, such as the Sun Yefang Economic Science Award, the Second Prize of the National Natural Science Award, and the National "May 1st" Labor Medal. Under the framework of nonlinear expectations, he has studied the law of large numbers and central limit theorem under non-independent conditions, discovered and obtained the explicit expression of the density of the nonlinear normal distribution, and proved the Felman conjecture and the conjecture that the Parrondo paradox exists in two-armed robots. His research achievements are known as the Nonlinear Chen-Epstein Central Limit Theorem (Nonlinear Chen-Epstein CLT) and the Chen-Epstein distribution. He has published a series of papers in top journals in probability and statistics, such as the Annals of Probability and JRSSB; top economic journals like Econometrica, Journal of Economic Theory, and Economic Theory; top control journals such as Automatica; and in the field of applied mathematics like Advances in Applied Mathematics.  

All faculty and students are welcome to attend!

Invited by: School of Mathematical Sciences

School of Mathematical Sciences  

April 28, 2025