  The practical performance of online stochastic gradient descent algorithms is
highly dependent on the chosen step size, which must be tediously hand-tuned in
many applications. The same is true for more advanced variants of stochastic
gradients, such as SAGA, SVRG, or AdaGrad. Here we propose to adapt the step
size by performing a gradient descent on the step size itself, viewing the
whole performance of the learning trajectory as a function of step size.
Importantly, this adaptation can be computed online at little cost, without
having to iterate backward passes over the full data.
