  In this paper, we propose a simple, fast and easy to implement algorithm
LOSSGRAD (locally optimal step-size in gradient descent), which automatically
modifies the step-size in gradient descent during neural networks training.
Given a function $f$, a point $x$, and the gradient $\nabla_x f$ of $f$, we aim
to find the step-size $h$ which is (locally) optimal, i.e. satisfies: $$
h=arg\,min_{t \geq 0} f(x-t \nabla_x f). $$ Making use of quadratic
approximation, we show that the algorithm satisfies the above assumption. We
experimentally show that our method is insensitive to the choice of initial
learning rate while achieving results comparable to other methods.
