aiqbench analysis
This research advances reinforcement learning by introducing an adaptive partitioning algorithm specifically designed for unbounded continuous state spaces in diffusion processes. The method dynamically refines discretization to balance exploration and approximation, providing theoretical regret bounds that extend existing guarantees to high-dimensional domains like multi-asset portfolio selection. While the applications touch on finance, the core contribution lies in solving fundamental challenges in machine learning theory for complex, continuous control systems.
Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes
arXiv:2512.14991v3 Announce Type: replace Abstract: 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 such as multi-asset mean-variance portfolio selection.
Abstract: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 such as multi-asset mean-variance portfolio selection.
Machine Learning (cs.LG); Optimization and Control (math.OC); Portfolio Management (q-fin.PM)
arXiv:2512.14991 [cs.LG]
(or arXiv:2512.14991v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2512.14991 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 258 words
Related coverage
Gauge Fields Modify Spectra and Induce Currents in Fokker-Planck Dynamics
Quantum Zeitgeist · Jun 15, 2026
Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling
arXiv · Oct 5, 2026
Spatially Adaptive Noise Injection
arXiv · Sep 17, 2026
MOSAIC: Mode- and Support-Aware Inference-Time Control of Robot Diffusion Models
arXiv · Oct 14, 2026