Adaptive Perturbation-Based Gradient Estimation for Discrete Latent Variable Models
This work addresses a specific bottleneck in gradient estimation for discrete latent variable models, offering an incremental improvement for researchers and practitioners in machine learning.
The paper tackles the sensitivity of Implicit Maximum Likelihood Estimation (IMLE) to finite difference step size by proposing Adaptive IMLE (AIMLE), which adaptively identifies the target distribution to trade off gradient information density and bias. The result shows that AIMLE produces faithful gradient estimates while requiring orders of magnitude fewer samples than other estimators in tasks like Learning to Explain and Discrete Variational Auto-Encoders.
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.