# Efficient Training of Neural SDEs Using Stochastic Optimal Control

arXiv: https://arxiv.org/abs/2505.17150 · HTML: https://mlsanity.com/paper/2505.17150/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 11 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 6 of 6)

- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs](https://mlsanity.com/paper/2312.10550/) (2023)
- [Variational Inference for SDEs Driven by Fractional Noise](https://mlsanity.com/paper/2310.12975/) (2023)
- [Deterministic particle flows for constraining stochastic nonlinear systems](https://mlsanity.com/paper/2112.05735/) (2021)
- [Statistical Inference for Stochastic Differential Equations with Memory](https://mlsanity.com/paper/1307.1164/) (2013)

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

- [Fractional Diffusion Bridge Models](https://mlsanity.com/paper/2511.01795/) (2025)
- [Deep Neural Networks Inspired by Differential Equations](https://mlsanity.com/paper/2510.09685/) (2025)
- [Variational Inference for L'evy Process-Driven SDEs via Neural Tilting](https://mlsanity.com/paper/2605.10934/) (2026)

## Abstract (arXiv)

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it is computationally challenging due to the iterative nature of maximizing the ELBO. In this work, we propose to decompose the control term into linear and residual non-linear components and derive an optimal control term for linear SDEs, using stochastic optimal control. Modeling the non-linear component by a neural network, we show how to efficiently train neural SDEs without sacrificing their expressive power. Since the linear part of the control term is optimal and does not need to be learned, the training is initialized at a lower cost and we observe faster convergence.