The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE) the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

本研究提出了第一个自适应梯度估计器AIMLE，用于复杂离散分布的IMLE，通过交换梯度信息密度和估计偏差的程度，自适应地确定目标分布，实验证明AIMLE能产生忠实的梯度估计，而需要比其他梯度估计器少数个数量级的样本。

离散潜变量模型自适应扰动梯度估计