Online Variance Reduction for Stochastic Optimization
This work addresses convergence issues in stochastic optimization for machine learning practitioners, offering a novel online approach that is incremental in improving sampling efficiency.
The paper tackles the problem of high variance in stochastic optimization by proposing an online algorithm for variance reduction through importance sampling, achieving competitive performance with the best fixed distribution in hindsight.
Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible remedy is to employ non-uniform importance sampling techniques, which take the structure of the dataset into account. In this work, we investigate a recently proposed setting which poses variance reduction as an online optimization problem with bandit feedback. We devise a novel and efficient algorithm for this setting that finds a sequence of importance sampling distributions competitive with the best fixed distribution in hindsight, the first result of this kind. While we present our method for sampling datapoints, it naturally extends to selecting coordinates or even blocks of thereof. Empirical validations underline the benefits of our method in several settings.