Learn then differentiate improves gradient estimates from simulations
Learn-Then-Differentiate Gradient Estimation
Machine Learning
Summary
Estimating gradients—how outputs change with inputs—is important in many computer science and engineering tasks. This paper explains a method where a model is first learned to approximate simulation outputs, and then that model is differentiated to estimate gradients. The authors provide a unified mathematical framework that clarifies what exactly is being differentiated and how accurate these gradient estimates can be. They also show that for various types of models, such as neural networks or kernel-based methods, the accuracy of the gradient estimates can approach the standard Monte Carlo rates if certain smoothness conditions hold.
What this means in practice
- •For machine learning engineers: Improve gradient calculations for simulation-based training when exact gradients are unavailable but data-driven models are feasible.
- •For financial modelers: Obtain more reliable sensitivity estimates from complex stochastic simulations by fitting smooth models and differentiating them.
A theory result. No direct application yet.
Authors
Nifei Lin, Qingkai Zhang, L. Jeff Hong
Abstract
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.