A Stochastic Gradient Descent Approach for Stochastic Optimal Control
A Stochastic Gradient Descent Approach for Stochastic Optimal Control
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DOI：
10.4208/eajam.190420.200420
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发表时间：
2020-06
影响因子：
1.2
通讯作者：
Richard Archibald
中科院分区：
文献类型：
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作者：
Richard Archibald
在这项工作中，我们引入了一种随机梯度下降方法，通过随机极大值原理来解决随机最优控制问题。驱动我们方法的动机是随机最优控制问题中成本函数的梯度处于期望之下，并且这种期望的数值计算需要完全计算前向后向随机微分方程组，这在计算上是昂贵的。通过随机梯度下降型优化所建议的单样本表示来评估期望，我们可以节省求解 FBSDE 时的计算量，并且只关注旨在确定最优控制过程的优化任务。 AMS 科目分类：65K10、49M37、49M25
In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. The motivation that drives our method is the gradient of the cost functional in the stochastic optimal control problem is under expectation, and numerical calculation of such an expectation requires fully computation of a system of forward backward stochastic differential equations, which is computationally expensive. By evaluating the expectation with single-sample representation as suggested by the stochastic gradient descent type optimisation, we could save computational efforts in solving FBSDEs and only focus on the optimisation task which aims to determine the optimal control process. AMS subject classifications: 65K10, 49M37, 49M25