Mathematics > Optimization and Control
[Submitted on 17 Mar 2023 (v1), last revised 11 Mar 2024 (this version, v3)]
Title:Recent Developments in Machine Learning Methods for Stochastic Control and Games
View PDF HTML (experimental)Abstract:Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of sophisticated numerical methods. Recently, computational methods based on machine learning have been developed for solving stochastic control problems and games. In this review, we focus on deep learning methods that have unlocked the possibility of solving such problems, even in high dimensions or when the structure is very complex, beyond what traditional numerical methods can achieve. We consider mostly the continuous time and continuous space setting. Many of the new approaches build on recent neural-network-based methods for solving high-dimensional partial differential equations or backward stochastic differential equations, or on model-free reinforcement learning for Markov decision processes that have led to breakthrough results. This paper provides an introduction to these methods and summarizes the state-of-the-art works at the crossroad of machine learning and stochastic control and games.
Submission history
From: Ruimeng Hu [view email][v1] Fri, 17 Mar 2023 21:53:07 UTC (14,648 KB)
[v2] Sun, 18 Feb 2024 18:18:07 UTC (7,320 KB)
[v3] Mon, 11 Mar 2024 04:59:57 UTC (7,320 KB)
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