南方科技大学知识苑(SUSTech KC): A branching particle system approximation for solving partially observed stochastic optimal control problems via stochastic maximum principle

题名	A branching particle system approximation for solving partially observed stochastic optimal control problems via stochastic maximum principle
作者	Wan, Hexiang 1; Wang, Guangchen 1; Xiong, Jie2,3
通讯作者	Xiong, Jie
发表日期	2023-03-01
DOI	10.1007/s40072-023-00294-w
发表期刊	STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS 影响因子和分区
ISSN	2194-0401
EISSN	2194-041X
摘要	This paper develops an efficient numerical algorithm for solving a class of partially observed stochastic optimal control problems with correlated noises. The main contribution of this paper is threefold: first, we introduce a relaxed system and assume the Roxin condition (convexity requirement) on coefficients. Then, an optimal relaxed system provides an optimal admissible control in a broader sense, and a relaxed control turns out to be a usual admissible control. Second, we transform the optimal control problem into an optimization problem for a convex functional by employing a projection operator. A stochastic gradient descent approach is then proposed and its convergence properties are demonstrated. Last but not least, we present a branching particle system (branching particle filter) to approximate the optimal filter. Due to the random nature of the coefficients in the Zakai equation, neither the dual approach nor the mild solution approach can be used. We devise a novel method for establishing the convergence of the branching particle system approximation, as well as its rate of convergence. This branching-type particle filter algorithm allows us to tackle non-Markovian environments. The major body of this paper concludes with a numerical case study.
关键词	Zakai equation Branching particle system Forward-backward stochastic differential equation Optimal control of partially observed system Maximum principle stochastic gradient decent
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	通讯
资助项目	NSFC["11831010","2022YFA1006103","2022YFA1006102"] ; NSF of Shandong Province["61925306","61821004"] ; null[ZR2019ZD42] ; null[ZR2020ZD24]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Statistics & Probability
WOS记录号	WOS:000955853200001
出版者	SPRINGER
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/523937
专题	理学院_数学系
作者单位	1.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 3.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China
通讯作者单位	数学系; 南方科技大学
推荐引用方式 GB/T 7714	Wan, Hexiang,Wang, Guangchen,Xiong, Jie. A branching particle system approximation for solving partially observed stochastic optimal control problems via stochastic maximum principle[J]. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS,2023.
APA	Wan, Hexiang,Wang, Guangchen,&Xiong, Jie.(2023).A branching particle system approximation for solving partially observed stochastic optimal control problems via stochastic maximum principle.STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS.
MLA	Wan, Hexiang,et al."A branching particle system approximation for solving partially observed stochastic optimal control problems via stochastic maximum principle".STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS (2023).