  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.

Machine Learning;Optimization and Control;Machine Learning