SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 326-350, February 2024.
Abstract. We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using the weak convergence technique of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, New York], together with the notion of relaxed control rule introduced by El Karoui, Huù Nguyen and Jeanblanc-Picqué [SIAM J. Control Optim., 26 (1988), pp. 1025–1061]. In particular, with a well chosen discrete-time control system, we obtain a first implementable numerical algorithm (with convergence) for the partially observed control problem. Moreover, our discrete-time approximation result would open the door to study convergence of more general numerical approximation methods, such as machine learning based methods. Finally, we illustrate our convergence result by numerical experiments on a partially observed control problem in a linear quadratic setting.

中文翻译：

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部分观测随机最优控制的离散时间逼近

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 326-350 页，2024 年 2 月。
摘要。我们考虑一类具有部分观测的随机最优控制问题，并通过离散时间控制问题研究它们的逼近。我们使用 Kushner 和 Dupuis 的弱收敛技术 [连续时间随机控制问题的数值方法，Springer，纽约] 以及 El Karoui、Huù Nguyen 和 Jeanblanc 引入的宽松控制规则的概念来建立收敛结果。 Picqué [SIAM J. Control Optim., 26 (1988), pp. 1025–1061]。特别是，通过精心选择的离散时间控制系统，我们获得了针对部分观察控制问题的第一个可实现的数值算法（具有收敛性）。此外，我们的离散时间近似结果将为研究更通用的数值近似方法（例如基于机器学习的方法）的收敛性打开大门。最后，我们通过线性二次设置中部分观察控制问题的数值实验来说明我们的收敛结果。