Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

Autor: Huyên Pham, Nicolas Langrené, Côme Huré, Achref Bachouch
Přispěvatelé: University of Oslo (UiO), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Data61 [Canberra] (CSIRO), Australian National University (ANU)-Commonwealth Scientific and Industrial Research Organisation [Canberra] (CSIRO), ANR-15-CE05-0024,CAESARS,Contrôle et simulation des systèmes électriques, interaction et robustesse(2015), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001))
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Statistics and Probability
FOS: Computer and information sciences
reinforcement learning
value iteration
General Mathematics
0211 other engineering and technologies
Computational Finance (q-fin.CP)
Machine Learning (stat.ML)
02 engineering and technology
01 natural sciences
[QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP]
FOS: Economics and business
010104 statistics & probability
Stochastic differential equation
Quantitative Finance - Computational Finance
Quadratic equation
[STAT.ML]Statistics [stat]/Machine Learning [stat.ML]
Statistics - Machine Learning
FOS: Mathematics
Reinforcement learning
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Valuation (algebra)
Stochastic control
021103 operations research
business.industry
Deep learning
Probability (math.PR)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Nonlinear system
Optimization and Control (math.OC)
Artificial intelligence
Markov decision process
Policy iteration algorithm
quantization
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
business
Algorithm
Mathematics - Probability
Zdroj: Methodology and Computing in Applied Probability
Methodology and Computing in Applied Probability, Springer Verlag, In press
ISSN: 1387-5841
1573-7713
Popis: This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.
Comment: 39 pages, 14 figures. Methodology and Computing in Applied Probability, Springer Verlag, In press
Databáze: OpenAIRE
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