Publications

Announcement

Differential Machine Learning

Differential machine learning (ML) is an extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels to inputs.

This image has an empty alt attribute; its file name is image.png — Brian Huge and Antoine Savine, Risk, October 2020

This image has an empty alt attribute; its file name is risk21-front-1.png — Brian Huge and Antoine Savine, Risk, October 2021

Differential ML is applicable in situations where high quality first order derivatives wrt training inputs are available. In the context of financial Derivatives and risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential machine learning, combined with AAD, provides extremely effective pricing and risk approximations. We can produce fast pricing analytics in models too complex for closed form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or regulations like XVA, CCR, FRTB or SIMM-MVA.

The first article is freely available here:

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, resulting in vastly improved performance, illustrated with a number of numerical examples, both idealized and real world. In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results. We also posted a TensorFlow implementation notebook.