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A Neural RDE approach for continuous-time non-Markovian stochastic control problems

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Title: A Neural RDE approach for continuous-time non-Markovian stochastic control problems
Authors: Hoglund, M
Rossi Ferrucci, E
Hernandez, C
Muguruza Gonzalez, A
Salvi, C
Sanchez-Betancourt, L
Zhang, Y
Item Type: Conference Paper
Abstract: We propose a novel framework for solving continuous-time non-Markovian stochastic optimal problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in control problems due to the time delay effects in the system coefficients or the driving noises, which leads to optimal control strategies depending explicitly on the historical trajectories of the system state. By modelling the control process as the solution of a Neural RDE driven by the state process, we show that the control-state joint dynamics are governed by an uncontrolled, augmented Neural RDE, allowing for fast Monte-Carlo estimation of the value function via trajectories simulation and memory-efficient back-propagation. We provide theoretical underpinnings for the proposed algorithmic framework by demonstrating that Neural RDEs serve as universal approximators for functions of random rough paths. Exhaustive numerical experiments on non-Markovian stochastic control problems are presented, which reveal that the proposed framework is time-resolution-invariant and achieves higher accuracy and better stability in irregular sampling compared to existing RNN-based approaches.
Issue Date: 23-Jul-2023
Date of Acceptance: 25-Jun-2023
URI: http://hdl.handle.net/10044/1/112267
Copyright Statement: © 2023 by the author(s).
Conference Name: International Conference on Machine Learning (ICML 23), New Frontiers in Learning, Control, and Dynamical Systems Workshop
Publication Status: Published
Start Date: 2023-07-23
Finish Date: 2023-07-29
Conference Place: Honolulu, Hawaii
Appears in Collections:Financial Mathematics
Mathematics