Amortized variance reduction for doubly stochastic objectives

• URL: http://arxiv.org/abs/2003.04125v1
• Date: Mon, 9 Mar 2020 13:23:14 GMT
• Title: Amortized variance reduction for doubly stochastic objectives
• Authors: Ayman Boustati, Sattar Vakili, James Hensman, ST John
• Abstract summary: Approximate inference in complex probabilistic models requires optimisation of doubly objective functions. Current approaches do not take into account how mini-batchity affects samplingity, 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 gradient computations.
• Score: 17.064916635597417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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