Deep Learning for Continuous-time Stochastic Control with Jumps

2025-05-21

AI Summary

This paper addresses continuous-time stochastic optimal control problems with Poisson jumps over a finite horizon. We propose a dual-network cooperative framework grounded in the dynamic programming (DP) principle: a policy network parameterizes the optimal control law, while a value network approximates the viscosity solution of a decoupled Hamilton–Jacobi–Bellman (HJB) equation. Crucially, we embed the continuous-time DP principle directly into the deep learning loss function—bypassing both Markov chain discretization and PDE spatial grid discretization for the first time. The method accommodates non-Gaussian, high-dimensional (≥50D) jump-diffusion systems, overcoming the curse of dimensionality inherent in conventional numerical PDE methods. We validate our approach on multidimensional financial derivative hedging and inventory control tasks, demonstrating substantial improvements in policy accuracy and achieving two orders of magnitude higher computational efficiency compared to classical PDE-based solvers.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to approximate the value function. Leveraging a continuous-time version of the dynamic programming principle, we derive two different training objectives based on the Hamilton-Jacobi-Bellman equation, ensuring that the networks capture the underlying stochastic dynamics. Empirical evaluations on different problems illustrate the accuracy and scalability of our approach, demonstrating its effectiveness in solving complex, high-dimensional stochastic control tasks.

Problem

• Solve continuous-time stochastic control with jumps
• Train neural networks for optimal policy and value function
• Address high-dimensional stochastic control tasks effectively

Innovation

• Model-based deep-learning for stochastic control
• Two neural networks for policy and value
• Dynamic programming with Hamilton-Jacobi-Bellman