Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912477334208512 |
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| author | Ji, Shaolin Xu, Rundong |
| author_facet | Ji, Shaolin Xu, Rundong |
| contents | This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The control-dependent diffusions make the traditional method of successive approximations (MSA) insufficient to reduce the value of cost functional in each iteration. Without adding extra terms over which to perform the Hamiltonian minimization, the MSA becomes sufficient by our novel error estimate involving a higher order backward adjoint equation. Under certain convexity assumptions on the coefficients (no convexity assumptions on the control domains), the value of the cost functional descends to the global minimum as the number of iterations tends to infinity. In particular, a convergence rate is available for a class of generalized linear-quadratic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01876 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems Ji, Shaolin Xu, Rundong Optimization and Control Numerical Analysis 93E20, 60H10, 60H30, 49M05 This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The control-dependent diffusions make the traditional method of successive approximations (MSA) insufficient to reduce the value of cost functional in each iteration. Without adding extra terms over which to perform the Hamiltonian minimization, the MSA becomes sufficient by our novel error estimate involving a higher order backward adjoint equation. Under certain convexity assumptions on the coefficients (no convexity assumptions on the control domains), the value of the cost functional descends to the global minimum as the number of iterations tends to infinity. In particular, a convergence rate is available for a class of generalized linear-quadratic systems. |
| title | Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems |
| topic | Optimization and Control Numerical Analysis 93E20, 60H10, 60H30, 49M05 |
| url | https://arxiv.org/abs/2207.01876 |