# Robust Reinforcement Learning under Diffusion Models for Data with Jumps

arXiv: https://arxiv.org/abs/2411.11697 · HTML: https://mlsanity.com/paper/2411.11697/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- 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)
- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Control randomisation approach for policy gradient and application to reinforcement learning in optimal switching](https://mlsanity.com/paper/2404.17939/) (2024)
- [Continuous-time q-Learning for Jump-Diffusion Models under Tsallis Entropy](https://mlsanity.com/paper/2407.03888/) (2024)
- [Entropy-Regularized Mean-Variance Portfolio Optimization with Jumps](https://mlsanity.com/paper/2312.13409/) (2023)
- [Robust Realized Integrated Beta Estimator with Application to Dynamic Analysis of Integrated Beta](https://mlsanity.com/paper/2301.06742/) (2023)

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

- [Continuous-time reinforcement learning: ellipticity enables model-free value function approximation](https://mlsanity.com/paper/2602.06930/) (2026)
- [An Actor-Critic Framework for Continuous-Time Jump-Diffusion Controls with Normalizing Flows](https://mlsanity.com/paper/2604.05398/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) has proven effective in solving complex decision-making tasks across various domains, but challenges remain in continuous-time settings, particularly when state dynamics are governed by stochastic differential equations (SDEs) with jump components. In this paper, we address this challenge by introducing the Mean-Square Bipower Variation Error (MSBVE) algorithm, which enhances robustness and convergence in scenarios involving significant stochastic noise and jumps. We first revisit the Mean-Square TD Error (MSTDE) algorithm, commonly used in continuous-time RL, and highlight its limitations in handling jumps in state dynamics. The proposed MSBVE algorithm minimizes the mean-square quadratic variation error, offering improved performance over MSTDE in environments characterized by SDEs with jumps. Simulations and formal proofs demonstrate that the MSBVE algorithm reliably estimates the value function in complex settings, surpassing MSTDE's performance when faced with jump processes. These findings underscore the importance of alternative error metrics to improve the resilience and effectiveness of RL algorithms in continuous-time frameworks.