# Recursive Regression with Neural Networks: Approximating the HJI PDE Solution

arXiv: https://arxiv.org/abs/1611.02739 · HTML: https://mlsanity.com/paper/1611.02739/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning](https://mlsanity.com/paper/2112.12288/) (2021)
- [SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems](https://mlsanity.com/paper/2201.05475/) (2022)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)

## Abstract (arXiv)

The majority of methods used to compute approximations to the Hamilton-Jacobi-Isaacs partial differential equation (HJI PDE) rely on the discretization of the state space to perform dynamic programming updates. This type of approach is known to suffer from the curse of dimensionality due to the exponential growth in grid points with the state dimension. In this work we present an approximate dynamic programming algorithm that computes an approximation of the solution of the HJI PDE by alternating between solving a regression problem and solving a minimax problem using a feedforward neural network as the function approximator. We find that this method requires less memory to run and to store the approximation than traditional gridding methods, and we test it on a few systems of two, three and six dimensions.