Deep Learning for High-Dimensional Continuous-Time Stochastic Optimal Control Without Explicit Solution

• 成果类型: Article
• 署名作者: Dupret, Jean-Loup; Hainaut, Donatien
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Universite Catholique Louvain
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.1102
• 发表日期: 2026
• 关键词: partial-differential-equations; NEURAL-NETWORK APPROACH; algorithm

摘要

This paper introduces the generalized policy iteration physics-informed neural network algorithm, a novel numerical scheme for solving continuous-time stochastic optimal control problems in high dimensions when the optimal control does not admit an explicit solution. The proposed iterative deep learning algorithm leverages physicsinformed neural networks on the Hamilton-Jacobi-Bellman residuals in an actor-critic fashion, which is built from the generalized policy iteration technique. It employs two separate neural networks to approximate both the value function and the multidimensional optimal control, achieving a global approximation of the optimal solution across all time and space that can be evaluated online rapidly. Theoretical guarantees on convergence and optimality are provided, whereas its accuracy and efficacy are empirically validated through two important numerical examples from operations research. In particular, we generalize the standard Almgren-Chriss model arising from optimal liquidation in finance by allowing for a price impact model with fully nonlinear temporary and permanent impact functions and by considering a multidimensional setting with numerous cointegrated assets.