The paper investigates continuous‑time stochastic control problems with unknown drift and running reward functions, using an exploratory reinforcement learning framework that incorporates relaxed controls and entropy regularization. It develops policy‑iteration algorithms based on probabilistic representations of the optimal value function and its gradient, proving convergence and demonstrating performance through numerical examples. The study also extends to a special case with control‑dependent diffusion, requiring a Hessian representation.
By Jin Ma, Gaozhan Wang, Jianfeng Zhang, Xunyu Zhou
arXiv:2604. 08580v2 Announce Type: replace-cross Abstract: Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints.
By Carles Domingo-Enrich, Jiequn Han
arXiv:2607. 06935v1 Announce Type: cross Abstract: Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory.
By Denis Belomestny, Alexander Gasnikov, Egor Gladin, Alexey Naumov, Artemy Rubtsov, Yuri Sapronov, Daniil Tiapkin, Nikita Yudin
arXiv:2607. 22201v1 Announce Type: cross Abstract: We introduce trajectory-regularized stochastic optimal control (TRSOC), which augments standard stochastic optimal control (SOC) with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions.
By Mintae Kim, Koushil Sreenath
arXiv:2404. 05185v4 Announce Type: replace-cross Abstract: This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity.
By Huafu Liao, Alp\'ar R. M\'esz\'aros, Chenchen Mou, Chao Zhou
arXiv:2602. 05379v2 Announce Type: replace-cross Abstract: Effective reinforcement learning (RL) for complex stochastic systems requires leveraging historical data to improve sample efficiency and accelerate policy optimization.
By Hua Zheng, Wei Xie, M. Ben Feng, Keilung Choy