# An Efficient High-Dimensional Gradient Estimator for Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2407.10065 · HTML: https://mlsanity.com/paper/2407.10065/

## Key facts

- Cited by 4 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 11 of its 28 references that are in the map.
- First posted on arXiv 14 Jul 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, 11 of 11)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence](https://mlsanity.com/paper/2105.08633/) (2021)
- [A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations](https://mlsanity.com/paper/2207.04496/) (2022)
- [Learning Stochastic Optimal Policies via Gradient Descent](https://mlsanity.com/paper/2106.03780/) (2021)

## Built on by (most cited first, 4 of 4)

- [Sample Complexity of Distributionally Robust Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2505.10007/) (2025)
- [Longitudinal Flow Matching for Trajectory Modeling](https://mlsanity.com/paper/2510.03569/) (2025)
- [Deep Neural Networks Inspired by Differential Equations](https://mlsanity.com/paper/2510.09685/) (2025)
- [Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data](https://mlsanity.com/paper/2601.05227/) (2026)

## Abstract (arXiv)

Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering, and neural SDEs. These models often feature system evolution coefficients that are parameterized by a high-dimensional vector θ ∈ ℝn, aiming to optimize expectations of the SDE, such as a value function, through stochastic gradient ascent. Consequently, designing efficient gradient estimators for which the computational complexity scales well with n is of significant interest. This paper introduces a novel unbiased stochastic gradient estimator--the generator gradient estimator--for which the computation time remains stable in n. In addition to establishing the validity of our methodology for general SDEs with jumps, we also perform numerical experiments that test our estimator in linear-quadratic control problems parameterized by high-dimensional neural networks. The results show a significant improvement in efficiency compared to the widely used pathwise differentiation method: Our estimator achieves near-constant computation times, increasingly outperforms its counterpart as n increases, and does so without compromising estimation variance. These empirical findings highlight the potential of our proposed methodology for optimizing SDEs in contemporary applications.