  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.
