论文标题
得分功能梯度估计器的最佳方差控制重要性加权边界
Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Bounds
论文作者
论文摘要
本文介绍了对重要性加权变分结合（IWAE）的分数功能梯度估计器的新结果。我们证明，在大$ k $（重要性示例数）的限制中，人们可以选择控制变量，以便估算器的信噪比（SNR）随着$ \ sqrt {k} $的增长而生长。这与标准的路径梯度估计器相反，该梯度估计器将SNR降低为$ 1/\ sqrt {k} $。根据我们的理论发现，我们开发了一种扩展Vimco的新型控制变量。从经验上讲，对于训练连续和离散的生成模型，所提出的方法会减少较高的差异，从而导致IWAE的SNR随着$ K $的增加而不依赖重新聚体化的技巧。该新型估计器具有竞争性的，在训练生成模型时，具有最新的无梯度估计器（例如重新加权的尾流（RWS））和热力学变化物镜（TVO）。
This paper introduces novel results for the score function gradient estimator of the importance weighted variational bound (IWAE). We prove that in the limit of large $K$ (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as $\sqrt{K}$. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as $1/\sqrt{K}$. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with $K$ without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.
