The goal of this paper is to accelerate the training of machine learning models, a critical challenge since the training of large-scale deep neural models can be computationally expensive. Stochastic gradient descent (SGD) and its variants are widely used to train deep neural networks. In contrast to traditional approaches that focus on tuning the learning rate, we propose a novel adaptive batch size SGD algorithm, DiveBatch, that dynamically adjusts the batch size. Adapting the batch size is challenging: using large batch sizes is more efficient due to parallel computation, but small-batch training often converges in fewer epochs and generalizes better. To address this challenge, we introduce a data-driven adaptation based on gradient diversity, enabling DiveBatch to maintain the generalization performance of small-batch training while improving convergence speed and computational efficiency. Gradient diversity has a strong theoretical justification: it emerges from the convergence analysis of SGD. Evaluations of DiveBatch on synthetic and CiFar-10, CiFar-100, and Tiny-ImageNet demonstrate that DiveBatch converges significantly faster than standard SGD and AdaBatch (1.06 -- 5.0x), with a slight trade-off in performance.

We study a new aggregation operator for gradients coming from a mini-batch for stochastic gradient (SG) methods that allows a significant speed-up in the case of sparse optimization problems. We call this method AdaBatch and it only requires a few lines of code change compared to regular mini-batch SGD algorithms. We provide a theoretical insight to understand how this new class of algorithms is performing and show that it is equivalent to an implicit per-coordinate rescaling of the gradients, similarly to what Adagrad methods can do. In theory and in practice, this new aggregation allows to keep the same sample efficiency of SG methods while increasing the batch size. Experimentally, we also show that in the case of smooth convex optimization, our procedure can even obtain a better loss when increasing the batch size for a fixed number of samples. We then apply this new algorithm to obtain a parallelizable stochastic gradient method that is synchronous but allows speed-up on par with Hogwild! methods as convergence does not deteriorate with the increase of the batch size. The same approach can be used to make mini-batch provably efficient for variance-reduced SG methods such as SVRG.