Approximation Based Variance Reduction for Reparameterization Gradients
This work addresses the problem of efficient optimization for complex variational models in machine learning, representing an incremental advancement in variance reduction techniques.
The paper tackles the challenge of optimizing flexible variational distributions in variational inference by introducing a control variate applicable to any reparameterizable distribution with known mean and covariance, such as Gaussians with arbitrary covariance structures, and empirically demonstrates large improvements in gradient variance and optimization convergence for non-factorized variational distributions.
Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme by minimizing the gradient estimator's variance. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.