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Solving Heterogeneous Agent Economic Models with High-Dimensional Dynamic Programming: A Neural Network Solution Method

Tabibpour, Alireza | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58544 (44)
  4. University: Sharif University of Technology
  5. Department: Management and Economics
  6. Advisor(s): Madanizadeh, Ali
  7. Abstract:
  8. This study proposes a novel method for solving heterogeneous economic models with high-dimensional dynamic programming using neural networks. Deep learning has proven highly effective in addressing computationally intensive problems, and due to their inherent structure, neural networks are well-suited for approximating complex, high-dimensional functions. This property makes them particularly attractive for solving heterogeneous economic models, and in particular, high-dimensional dynamic programming problems. Among recent developments in computer science, the Set Transformer architecture stands out as one of the most powerful and efficient neural network structures for such tasks. Accordingly, the neural network used in this study is based on the Set Transformer architecture Classical dynamic programming methods often face serious computational barriers due to the curse of dimensionality, and prior neural network-based approaches—such as Deep Sets—lack the capacity to model complex, nonlinear interactions in high-dimensional state spaces. In contrast, the Set Transformer, by leveraging "attention mechanisms" and "induced set attention blocks", overcomes these limitations and enables more accurate approximation of permutation-invariant functions. This makes it especially suitable for heterogeneous economic models that exhibit such symmetries. To evaluate the proposed method, we implement an economic model and train the network using an Euler residual minimization approach, ensuring both consistency with economic theory and strong performance in terms of accuracy and scalability. The model used is well-established in the literature, enabling meaningful comparison with previous methods. Numerical results, in both linear-quadratic settings and nonlinear scenarios, indicate that the proposed method significantly outperforms previous architectures such as Deep Sets, and show that the deviation from Euler equation can be reduced 100 times compared to the previous methods. These findings highlight the potential of deep learning—and the Set Transformer in particular—as a powerful computational tool for analyzing the complex dynamics of modern economic models
  9. Keywords:
  10. Neural Networks ; Attention Mechanism ; Set Transformer Architecture ; Permutation Invariance ; High-Dimensional Dynamic Programming (HDDP) ; Heterogeneous Agent Models

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