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荔园杰出学者讲座第三十六期

讲座题目:  Solving Hamilton-Jacobi-Bellman equations using at most four-armed slot machines

主讲人：陈增敬 教授（山东大学）

讲座时间：2025年4月29日上午10：00-11：00

讲座地点：深圳大学粤海校区汇星楼一号教室

内容摘要：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.

主讲人简介：陈增敬，山东大学数学院教授 ，山东大学中泰证券金融研究院院长。主要从事金融数学、倒向随机微分方程、非线性期望、计量经济学等领域的研究。曾先后获得孙冶方经济科学奖，国家自然科学二等奖，全国“五一”劳动奖章，等奖项。在非线性期望框架下，研究了非独立条件下的大数定理和中心极限定理，发现和得到了非线性正态分布分布密度的显示表达式，证明了Felman猜想和双臂机器人中存在Parrondo悖论的猜想。研究成果被称为非线性 Chen-Epstein 中心极限定理（Nonlinear Chen-Epstein CLT）和 Chen-Epstein 分布（Chen-Epstein distribution）。先后在概率统计顶刊Annals of Probability、JRSSB；经济顶刊 Econometrica、Journal of Economic Theory、 Economic Theory；控制顶刊Automatica和应用数学Advances in Applied Mathematics 等期刊发表了一系列论文。

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2025年4月28日