Amortized variance reduction for doubly stochastic objectives

TL;DR

This paper introduces a novel amortized control variate method using recognition networks to effectively reduce variance in doubly stochastic objectives, improving the efficiency of inference in complex probabilistic models.

Contribution

It proposes a recognition network-based approach to approximate optimal control variates, accounting for mini-batch stochasticity without extra gradient computations.

Findings

Reduced gradient variance in deep Gaussian processes

Improved convergence speed in stochastic optimization

Effective variance reduction in logistic regression

Abstract

Approximate inference in complex probabilistic models such as deep Gaussian processes requires the optimisation of doubly stochastic objective functions. These objectives incorporate randomness both from mini-batch subsampling of the data and from Monte Carlo estimation of expectations. If the gradient variance is high, the stochastic optimisation problem becomes difficult with a slow rate of convergence. Control variates can be used to reduce the variance, but past approaches do not take into account how mini-batch stochasticity affects sampling stochasticity, resulting in sub-optimal variance reduction. We propose a new approach in which we use a recognition network to cheaply approximate the optimal control variate for each mini-batch, with no additional model gradient computations. We illustrate the properties of this proposal and test its performance on logistic regression and deep Gaussian processes.