# An Efficient Policy Iteration Algorithm for Dynamic Programming Equations

arXiv: https://arxiv.org/abs/1308.2087 · HTML: https://mlsanity.com/paper/1308.2087/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2013.

## Built on by (most cited first, 2 of 2)

- [Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs](https://mlsanity.com/paper/2207.09299/) (2022)
- [Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems](https://mlsanity.com/paper/2505.00909/) (2025)

## Abstract (arXiv)

We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear convergence in many relevant cases provided the initial guess is sufficiently close to the solution. In many cases, this limitation degenerates into a behavior similar to a value iteration method, with an increased computation time. The new scheme circumvents this problem by combining the advantages of both algorithms with an efficient coupling. The method starts with a value iteration phase and then switches to a policy iteration procedure when a certain error threshold is reached. A delicate point is to determine this threshold in order to avoid cumbersome computation with the value iteration and, at the same time, to be reasonably sure that the policy iteration method will finally converge to the optimal solution. We analyze the methods and efficient coupling in a number of examples in dimension two, three and four illustrating its properties.