Learn-Then-Differentiate Gradient Estimation

arXiv:2609.38842v1 Announce Type: cross 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.

Related

• Multi-modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation
• A robust and adaptive MPC formulation for Gaussian process models
• Truncated automatic sparse differentiation for machine learning interatomic potentials

Source: arXiv cs.LG | 2026-10-01