# On the grid-sampling limit SDE

arXiv: https://arxiv.org/abs/2410.07778 · HTML: https://mlsanity.com/paper/2410.07778/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 8 of 8)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [q-Learning in Continuous Time](https://mlsanity.com/paper/2207.00713/) (2022)
- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Exploratory LQG Mean Field Games with Entropy Regularization](https://mlsanity.com/paper/2011.12946/) (2020)
- [Regularity and stability of feedback relaxed controls](https://mlsanity.com/paper/2001.03148/) (2020)
- [Entropy-Regularized Mean-Variance Portfolio Optimization with Jumps](https://mlsanity.com/paper/2312.13409/) (2023)
- [A random measure approach to reinforcement learning in continuous time](https://mlsanity.com/paper/2409.17200/) (2024)

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

- [Accuracy of Discretely Sampled Stochastic Policies in Continuous-time Reinforcement Learning](https://mlsanity.com/paper/2503.09981/) (2025)
- [Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations](https://mlsanity.com/paper/2604.27372/) (2026)
- [Discretization error from regularized Reinforcement Learning to continuous-time stochastic control](https://mlsanity.com/paper/2604.21179/) (2026)

## Abstract (arXiv)

In our recent work [3] we introduced the grid-sampling SDE as a proxy for modeling exploration in continuous-time reinforcement learning. In this note, we provide further motivation for the use of this SDE and discuss its wellposedness in the presence of jumps.