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Convergence of a ro...
Convergence of a robust deep FBSDE method for stochastic control
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- Andersson, Kristoffer (författare)
- Stichting Centrum voor Wiskunde & Informatica (CWI)
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- Andersson, Adam, 1979 (författare)
- Chalmers tekniska högskola,Chalmers University of Technology
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- Oosterlee, Cornelis (författare)
- Universiteit Utrecht,Utrecht University
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(creator_code:org_t)
- 2023
- 2023
- Engelska.
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Ingår i: SIAM Journal of Scientific Computing. - 1064-8275 .- 1095-7197. ; 45:1, s. A226-A255
- Relaterad länk:
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- In this paper, we propose a deep learning based numerical scheme for strongly coupled FBSDEs, stemming from stochastic control. It is a modification of the deep BSDE method in which the initial value to the backward equation is not a free parameter, and with a new loss function being the weighted sum of the cost of the control problem, and a variance term which coincides with the mean squared error in the terminal condition. We show by a numerical example that a direct extension of the classical deep BSDE method to FBSDEs, fails for a simple linear-quadratic control problem, and motivate why the new method works. Under regularity and boundedness assumptions on the exact controls of time continuous and time discrete control problems, we provide an error analysis for our method. We show empirically that the method converges for three different problems, one being the one that failed for a direct extension of the deep BSDE method.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- stochastic control
- deep learning
- FBSDE
Publikations- och innehållstyp
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- ref (ämneskategori)
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