勷勤数学•专家报告

题      目：Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes

报  告  人： 金含清 教授  (邀请人：杨舟)

                                                牛津大学

时      间： 8月25日  10：30-11:30

地     点：数科院西楼二楼会议室

报告人简介:

          金含清，博士，牛津大学教授，牛津大学NIE金融大数据实验室主任。主要从事金融统计、金融数学、行为金融学等方面的研究，在Journal of Economic Theory、Mathematical Finance、SIAM Journal on Control and Optimization、Mathematics of Operations Research等Top期刊发表了数十篇高水平的论文，其中有多篇为被高引论文。担任多个金融数学Top期刊的编委。

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.

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