Stochastic Automatic Differentiation : Efficient Tapeless Implementation of Automatic Differentiation for Monte-Carlo Simulations

In this paper we present an efficient implementation of automatic differentiations of random variables (see 'https://ssrn.com/abstract=2995695' https://ssrn.com/abstract=2995695).Using this implementation can increase the speed of the calculation of the automatic differentiation and reduce the memory requirements. In some cases this approach may give surprising results: We give examples where the the calculation of all partial derivatives is 10000-times faster compared to the calculation of the value and the memory footprint is the same. A trivial example is the AAD calculation of a sum of random variables. While this is an operator on a random variable (i.e., a vector of thousands of Monte-Carlo samples), the partial derivatives are just scalars