# DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks

arXiv: https://arxiv.org/abs/2112.14377 · HTML: https://mlsanity.com/paper/2112.14377/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 90 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games](https://mlsanity.com/paper/1912.01809/) (2019)
- [Deep Fictitious Play for Stochastic Differential Games](https://mlsanity.com/paper/1903.09376/) (2019)

## Built on by (most cited first, 11 of 11)

- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [Deep Learning for Solving and Estimating Dynamic Macro-Finance Models](https://mlsanity.com/paper/2305.09783/) (2023)
- [Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning](https://mlsanity.com/paper/2303.04833/) (2023)
- [Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models](https://mlsanity.com/paper/2406.13726/) (2024)
- [EconGym: A Scalable AI Testbed with Diverse Economic Tasks](https://mlsanity.com/paper/2506.12110/) (2025)
- [Structural Reinforcement Learning for Heterogeneous Agent Macroeconomics](https://mlsanity.com/paper/2512.18892/) (2025)
- [Deep Learning for Dynamic Programming with Recursive Utility](https://mlsanity.com/paper/2607.04278/) (2026)
- [Optimal Trade and Industrial Policies in the Global Economy: A Deep Learning Framework](https://mlsanity.com/paper/2407.17731/) (2024)
- [A Machine Learning Algorithm for Finite-Horizon Stochastic Control Problems in Economics](https://mlsanity.com/paper/2411.08668/) (2024)
- [Recurrent Structural Policy Gradient for Partially Observable Mean Field Games](https://mlsanity.com/paper/2602.20141/) (2026)

## Abstract (arXiv)

An efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), is proposed for solving high dimensional heterogeneous agent models with aggregate shocks. The state distribution is approximately represented by a set of optimal generalized moments. Deep neural networks are used to approximate the value and policy functions, and the objective is optimized over directly simulated paths. In addition to being an accurate global solver, this method has three additional features. First, it is computationally efficient in solving complex heterogeneous agent models, and it does not suffer from the curse of dimensionality. Second, it provides a general and interpretable representation of the distribution over individual states, which is crucial in addressing the classical question of whether and how heterogeneity matters in macroeconomics. Third, it solves the constrained efficiency problem as easily as it solves the competitive equilibrium, which opens up new possibilities for studying optimal monetary and fiscal policies in heterogeneous agent models with aggregate shocks.