Backpropagation through the Void: Optimizing control variates for black-box gradient estimation

Gradient-based optimization is the foundation of deep learning and reinforcement learning, but is difficult to apply when the mechanism being optimized is unknown or not differentiable. We introduce a general framework for learning low-variance, unbiased gradient estimators, applicable to black-box functions of discrete or continuous random variables. Our method uses gradients of a surrogate neural network to construct a control variate, which is optimized jointly with the original parameters. We demonstrate this framework for training discrete latent-variable models. We also give an unbiased, action-conditional extension of the advantage actor-critic reinforcement learning algorithm.