# Deep Learning Methods for Mean Field Control Problems with Delay

arXiv: https://arxiv.org/abs/1905.00358 · HTML: https://mlsanity.com/paper/1905.00358/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

## Built on by (most cited first, 25 of 25)

- [Scalable Deep Reinforcement Learning Algorithms for Mean Field Games](https://mlsanity.com/paper/2203.11973/) (2022)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Mean-field neural networks: learning mappings on Wasserstein space](https://mlsanity.com/paper/2210.15179/) (2022)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guarantee](https://mlsanity.com/paper/2302.05816/) (2023)
- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Deep Learning for Principal-Agent Mean Field Games](https://mlsanity.com/paper/2110.01127/) (2021)
- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [Model-free policy gradient for discrete-time mean-field control](https://mlsanity.com/paper/2601.11217/) (2026)
- [Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators](https://mlsanity.com/paper/2510.20017/) (2025)
- [Recurrent Neural Networks for Stochastic Control Problems with Delay](https://mlsanity.com/paper/2101.01385/) (2021)
- [Convergence of the Deep Galerkin Method for Finite State Mean Field Control Problems](https://mlsanity.com/paper/2405.13346/) (2024)
- [Operator Learning for Families of Finite-State Mean-Field Games](https://mlsanity.com/paper/2602.13169/) (2026)
- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)
- [Solving a class of stochastic optimal control problems by physics-informed neural networks](https://mlsanity.com/paper/2402.15592/) (2024)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type](https://mlsanity.com/paper/2210.00874/) (2022)
- [Reimagining Demand-Side Management with Mean Field Learning](https://mlsanity.com/paper/2302.08190/) (2023)
- [Networked Communication for Decentralised Agents in Mean-Field Games](https://mlsanity.com/paper/2306.02766/) (2023)
- [Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms](https://mlsanity.com/paper/2307.06450/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)

## Abstract (arXiv)

We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly parameterize the optimal control using neural networks, the other is based on numerically solving the McKean-Vlasov forward anticipated backward stochastic differential equation (MV-FABSDE) system. In addition, we establish a necessary and sufficient stochastic maximum principle for this class of mean field control problems with delay based on the differential calculus on function of measures, as well as existence and uniqueness results for the associated MV-FABSDE system.