# Diffusive limit approximation of pure jump optimal ergodic control problems

arXiv: https://arxiv.org/abs/2209.15284 · HTML: https://mlsanity.com/paper/2209.15284/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2022.

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

- [Near-continuous time Reinforcement Learning for continuous state-action spaces](https://mlsanity.com/paper/2309.02815/) (2023)

## Abstract (arXiv)

Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation error is governed by the H"older continuity of the Hessian matrix of the solution to the limit ergodic partial differential equation. This extends to this context the results of [1] obtained for finite horizon problems. We also explain how to construct a first order error correction term under appropriate smoothness assumptions. Finally, we quantify the error induced by the use of the Markov control policy constructed from the numerical finite difference scheme associated to the limit diffusive problem, this seems to be new in the literature and of its own interest. This approach permits to reduce very significantly the numerical resolution cost.