Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes

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• Hanqing Jin (University of Oxford)
• Tuesday 11 November 2025, 11:30-12:10
• Seminar Room 1, Newton Institute.

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SCLW01 - Bridging Stochastic Control And Reinforcement Learning: Theories and Applications

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 discretisation 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. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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