On the grid-sampling limit SDE

TL;DR

This paper discusses the grid-sampling stochastic differential equation (SDE) as a model for exploration in continuous-time reinforcement learning, emphasizing its motivation and well-posedness with jumps.

Contribution

It provides further motivation for the grid-sampling SDE and analyzes its well-posedness in the presence of jumps, extending prior work.

Findings

Supports the use of grid-sampling SDE as exploration proxy

Establishes conditions for well-posedness with jumps

Enhances understanding of SDE modeling in RL

Abstract

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.