  Machine learning practitioners invest significant manual and computational
resources in finding suitable learning rates for optimization algorithms. We
provide a probabilistic motivation, in terms of Gaussian inference, for popular
stochastic first-order methods. As an important special case, it recovers the
Polyak step with a general metric. The inference allows us to relate the
learning rate to a dimensionless quantity that can be automatically adapted
during training by a control algorithm. The resulting meta-algorithm is shown
to adapt learning rates in a robust manner across a large range of initial
values when applied to deep learning benchmark problems.
