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Deep Learning Methods for Mean Field Control Problems with Delay

arXiv 1905.00358 ↗First posted 1 May 2019math.OCcited by 24

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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.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 May 2019.

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Citing papers per year: 2021: 6; 2022: 4; 2023: 5; 2024: 5; 2025: 1; 2026: 3.

24 papers.

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  1. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  2. 2021Scaling up Mean Field Games with Online Mirror Descentcited by 29
  3. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  4. 2022Mean-field neural networks: learning mappings on Wasserstein spacecited by 15
  5. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 14
  6. 2022Mean-field neural networks-based algorithms for McKean-Vlasov control problems *cited by 9
  7. 2023A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guaranteecited by 6
  8. 2024Deep Backward and Galerkin Methods for the Finite State Master Equationcited by 6
  9. 2021Deep Learning for Principal-Agent Mean Field Gamescited by 5
  10. 2021Deep Signature FBSDE Algorithmcited by 4
  11. 2025Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operatorscited by 3
  12. 2026Model-free policy gradient for discrete-time mean-field controlcited by 3
12 more
  1. 2021Recurrent Neural Networks for Stochastic Control Problems with Delaycited by 2
  2. 2024Convergence of the Deep Galerkin Method for Finite State Mean Field Control Problemscited by 2
  3. 2026Operator Learning for Families of Finite-State Mean-Field Gamescited by 2
  4. 2026Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Controlcited by 2
  5. 2023Deep Learning for Mean Field Optimal Transportcited by 1
  6. 2024Solving a class of stochastic optimal control problems by physics-informed neural networkscited by 1
  7. 2024Learning to Stop: Deep Learning for Mean Field Optimal Stoppingcited by 1
  8. 2022Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Typecited by 0
  9. 2023Reimagining Demand-Side Management with Mean Field Learningcited by 0
  10. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  11. 2023Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithmscited by 0
  12. 2024A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agentscited by 0