mlsanityData to 7 Oct 2026

Neural Operators Can Play Dynamic Stackelberg Games

arXiv 2411.09644 ↗First posted 14 Nov 2024math.OC cs.LG cs.NAcited by 5

Not on the map. Why?

Abstract (arXiv)

Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the textitfollower's best-response operator can be approximately implemented by an textitattention-based neural operator, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 38 of its 94 references that are in the map. First posted on arXiv 14 Nov 2024.

Builds on

38 of 94 references.

References · 38

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  6. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  7. 2021Choose a Transformer: Fourier or Galerkincited by 333
  8. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  9. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  10. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  11. 2019Universal Approximation with Deep Narrow Networkscited by 198
  12. 2021Optimal Approximation Rate of ReLU Networks in terms of Width and Depthcited by 95
26 more
  1. 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
  2. 2023Neural Inverse Operators for Solving PDE Inverse Problemscited by 61
  3. 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
  4. 2021Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equationscited by 44
  5. 2023Operator learning with PCA-Net: upper and lower complexity boundscited by 44
  6. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  7. 2021Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neuronscited by 41
  8. 2024Continuum Attention for Neural Operatorscited by 39
  9. 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
  10. 2022Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuitiescited by 29
  11. 2023Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agentscited by 25
  12. 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
  13. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  14. 2022Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysiscited by 22
  15. 2019Deep learning architectures for nonlinear operator functions and nonlinear inverse problemscited by 17
  16. 2024Mixtures of Neural Operators Reduce Active Complexity in Operator Learningcited by 16
  17. 2019Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systemscited by 12
  18. 2022Oracles & Followers: Stackelberg Equilibria in Deep Multi-Agent Reinforcement Learningcited by 12
  19. 2020Optimal incentives to mitigate epidemics: a Stackelberg mean field game approachcited by 8
  20. 2016A tale of a Principal and many many Agentscited by 7
  21. 2023An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learningcited by 7
  22. 2024Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularitycited by 7
  23. 2023A Machine Learning Method for Stackelberg Mean Field Gamescited by 4
  24. 2020Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemiccited by 1
  25. 2023Time-inconsistent contract theorycited by 1
  26. 2024Closed-loop equilibria for Stackelberg games: a story about stochastic targetscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 1.

5 papers.

  1. 2025Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programscited by 5
  2. 2025Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operatorscited by 3
  3. 2025One model to solve them all: 2BSDE families via neural operatorscited by 3
  4. 2025Deep Neural Operator Learning for Probabilistic Modelscited by 2
  5. 2026NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processescited by 0