# Learn-Then-Differentiate Gradient Estimation

arXiv: https://arxiv.org/abs/2609.38842 · HTML: https://mlsanity.com/paper/2609.38842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 64 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 1 of 1)

- [Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutions](https://mlsanity.com/paper/2512.06270/) (2025)

## Abstract (arXiv)

Learn-then-differentiate (LTD) estimates gradients by fitting a model to simulation outputs and differentiating it. We develop a unified framework explaining what LTD differentiates and how accurately it estimates gradients. For models with a weighted representation, LTD differentiates a learned representation of the underlying probability measure. We then show how accuracy guarantees for fitted models translate into guarantees for gradients and higher-order derivatives, with rates approaching the standard Monte Carlo rate under suitable smoothness conditions. The framework recovers established results for kernel regression, local polynomial regression, and kernel ridge regression, and yields further guarantees for multiple kernel learning and smooth neural networks. These results provide a common foundation for understanding and analyzing LTD across learning methods.