# Policy iteration for the deterministic control problems -- a viscosity approach

arXiv: https://arxiv.org/abs/2301.00419 · HTML: https://mlsanity.com/paper/2301.00419/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2023.

## Built on by (most cited first, 7 of 7)

- [Regret of exploratory policy improvement and q-learning](https://mlsanity.com/paper/2411.01302/) (2024)
- [Hamilton-Jacobi Based Policy-Iteration via Deep Operator Learning](https://mlsanity.com/paper/2406.10920/) (2024)
- [Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline](https://mlsanity.com/paper/2605.06583/) (2026)
- [Physics-Informed Neural Networks for Optimal Vaccination Plan in SIR Epidemic Models](https://mlsanity.com/paper/2502.19890/) (2025)
- [Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration](https://mlsanity.com/paper/2507.15455/) (2025)
- [Physics-Informed Policy Iteration for High-Dimensional Hamilton--Jacobi--Bellman Equations: Interior Error Bounds without Boundary Data](https://mlsanity.com/paper/2508.01718/) (2025)
- [Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations](https://mlsanity.com/paper/2605.07116/) (2026)

## Abstract (arXiv)

This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by adding a viscosity term via finite differences in space. We prove that PI for the semi-discrete scheme converges exponentially fast, and provide a bound on the error induced by the semi-discrete scheme. We also consider the discrete space-time scheme, where both space and time are discretized. Convergence rate of PI and the discretization error are studied.