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Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

We study continuous-time and possibly high-dimensional stochastic control problems where drift coefficients and running reward functions are unknown. Due to these missing model primitives, we take the exploratory, reinforcement learning (RL) framework of Wang, Zariphopoulou, and Zhou(2020) with relaxed controls and entropy regularization. The objective is to develop theoretically grounded, efficient and scalable RL algorithms to learn both the optimal value functions (which also solve the exploratory HJB equation) and optimal exploratory feedback control policies. When the diffusion coefficien

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