# Deep Learning for Dynamic Programming with Recursive Utility

arXiv: https://arxiv.org/abs/2607.04278 · HTML: https://mlsanity.com/paper/2607.04278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 80 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 2 of 2)

- [DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks](https://mlsanity.com/paper/2112.14377/) (2021)
- [Stochastic dynamic programming under recursive Epstein-Zin preferences](https://mlsanity.com/paper/2410.19181/) (2024)

## Built on by (most cited first, 1 of 1)

- [Deep Learning for Dynamic Programming with Recursive Utility Using First-order Conditions](https://mlsanity.com/paper/2607.09461/) (2026)

## Abstract (arXiv)

We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit representation and the Bellman equation contains a certainty equivalent that is difficult to evaluate. The CEL algorithm learns this certainty-equivalent value directly with neural networks and jointly approximates value functions, policy functions, and certainty-equivalent functions. The CEL algorithm is mesh-free and simulation-based, allowing high-dimensional state and control spaces, and does not rely on Euler equations, first-order conditions, or differentiability of the state transition function. The CEL algorithm also works for dynamic programming problems with expected utility as expected utility is a special case of recursive utility. We apply the CEL to discounted linear exponential quadratic Gaussian control, small-noise robust control, Epstein-Zin DSGE, and multivariate strategic asset allocation problems. Compared with closed-form and VFI-based benchmarks, the CEL delivers accurate value and policy approximations, remains effective in high-dimensional problems, achieves accuracy comparable to VFI in the small-noise robust-control case, and produces out-of-sample Bellman errors and Euler or first-order residuals that are in the range from 1.0e-4 to 1.0e-3 for most problems.