Amortized variance reduction for doubly stochastic objectives
This addresses slow convergence in stochastic optimization for probabilistic modeling, offering a more efficient variance reduction method, though it appears incremental as it builds on existing control variate techniques.
The paper tackles the problem of high gradient variance in optimizing doubly stochastic objectives for approximate inference in complex probabilistic models, proposing a recognition network to approximate optimal control variates per mini-batch without extra gradient computations, resulting in improved performance on logistic regression and deep Gaussian processes.
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.