AR-DAE: Towards Unbiased Neural Entropy Gradient Estimation

Entropy is ubiquitous in machine learning, but it is in general intractable to compute the entropy of the distribution of an arbitrary continuous random variable. In this paper, we propose the amortized residual denoising autoencoder (AR-DAE) to approximate the gradient of the log density function, which can be used to estimate the gradient of entropy. Amortization allows us to significantly reduce the error of the gradient approximator by approaching asymptotic optimality of a regular DAE, in which case the estimation is in theory unbiased. We conduct theoretical and experimental analyses on the approximation error of the proposed method, as well as extensive studies on heuristics to ensure its robustness. Finally, using the proposed gradient approximator to estimate the gradient of entropy, we demonstrate state-ofthe-art performance on density estimation with variational autoencoders and continuous control with soft actor-critic. 0.001, 0.0001 0.001, 0.0001 β-annealing no no no no, 50000 no, 50000 e-train with train+val no no no no yes Evaluation polyak (decay) -no no no 0.998 polyak (start interation) -no no no 0, 1000, 5000, 10000 neval -40000 40000 20000 20000 Table 8. Hyperparameters for the VAE experiments. toy is the 25 Gaussian dataset. dbmnist and sbmnist are dynamically and statically binarized MNIST, respectively.