In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs-directed acyclic graphs that include both deterministic functions and conditional probability distributions-and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.
REF also write the gradient in the form given in Eq. 12 to automatically estimate the gradient through a backpropagation algorithm in the context of stochastic computation graphs.
Gradient Estimation Using Stochastic Computation Graphs
ArXiv
ArXiv
Mathematics Computer Science