报告题目：Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes
报 告 人：金含清 副教授（牛津大学）
报告时间：2026年8月12日（星期三）9:00—10:00
报告地点：数学科学学院114
校内联系人：李娜 教授 联系方式：84708354
报告摘要：We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards—settings that arise naturally in finance, economics, and operations research. To overcome the challenges of continuous and high-dimensional domains, we introduce a model-based algorithm that adaptively partitions the joint state–action space. The algorithm maintains estimators of drift, volatility, and rewards within each partition, refining the discretization whenever estimation bias exceeds statistical confidence. This adaptive scheme balances exploration and approximation, enabling efficient learning in unbounded domains. Our analysis establishes regret bounds that depend on the problem horizon, state dimension, reward growth order, and a newly defined notion of zooming dimension tailored to unbounded diffusion processes. The bounds recover existing results for bounded settings as a special case, while extending theoretical guarantees to a broader class of diffusion-type problems. Finally, we validate the effectiveness of our approach through numerical experiments, including applications to high-dimensional problems.
报告人简介：Dr. Jin (金含清) is an associate professor in the Mathematical Institute at the University of Oxford. He received his MSc in Mathematics from Nankai University in 2001, and the PhD in Financial Engineering from Chinese University of Hong Kong in 2004. He staved in the department as a postdoctoral fellow for two years after graduation, and then worked in the Math department in the National University of Singapore as an assistant professor. In Jan 2008, he moved to the University of Oxford. His research interests include Mathematical Finance, Operation Research, and Stochastic Analysis. Recently his research expanded to Machine Learning and Decentralised Finance.
