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.

翻译：在深度学习架构中集成离散算法组件具有广泛的应用前景。近期，研究者通过结合扰动隐式微分与路径梯度估计器，提出了针对离散指数族分布的梯度估计方法——隐式最大似然估计（IMLE, Niepert, Minervini and Franceschi 2021）。然而，由于梯度估计采用有限差分近似，该方法对有限差分步长的选择尤为敏感，而该参数需由用户手动设定。本文提出自适应隐式最大似然估计（AIMLE），这是首个面向复杂离散分布的自适应梯度估计器：通过权衡梯度信息密度与梯度估计偏差程度，自适应地确定IMLE的目标分布。我们在合成数据样本以及学习解释、离散变分自编码器、神经关系推理等任务中进行了实证评估。实验结果表明，本方法在产生可靠梯度估计的同时，所需采样数量比现有梯度估计器少数个数量级。