This article adopts a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where the drift and diffusion terms in the dynamics may depend on both the state and control. Based on the Bellman’s dynamic programming principle, we presented an online RL algorithm to attain optimal control with partial system information. This algorithm computes the optimal control, rather than estimates the system coefficients, and solves the related Riccati equation. It only requires local trajectory information, which significantly simplifies the calculation process. We shed light on our theoretical findings using two numerical examples.

中文翻译：

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随机线性二次最优控制问题：一种强化学习方法

本文采用强化学习 (RL) 方法来解决无限视界连续时间随机线性二次问题，其中动力学中的漂移和扩散项可能取决于状态和控制。基于贝尔曼动态规划原理，我们提出了一种在线强化学习算法，利用部分系统信息实现最优控制。该算法计算最优控制，而不是估计系统系数，并求解相关的 Riccati 方程。它只需要局部轨迹信息，大大简化了计算过程。我们使用两个数值示例阐明了我们的理论发现。