Title: DASGrad: Double Adaptive Stochastic Gradient. Abstract: Adaptive moment methods have been remarkably successful for optimization under the presence of high dimensional or sparse gradients, in parallel to this, adaptive sampling probabilities for SGD have allowed optimizers to improve convergence rates by prioritizing examples to learn efficiently. Numerous applications in the past have implicitly combined adaptive moment methods with adaptive probabilities yet the theoretical guarantees of such procedures have not been explored. We formalize double adaptive stochastic gradient methods DASGrad as an optimization technique and analyze its convergence improvements in a stochastic convex optimization setting, we provide empirical validation of our findings with convex and non convex objectives. We observe that the benefits of the method increase with the model complexity and variability of the gradients, and we explore the resulting utility in extensions to transfer learning. 