Gradient descent revisited via an adaptive online learning rate

Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the gradient descent algorithm in the which the learning rate is not fixed. Instead, we learn the learning rate itself, either by another gradient descent (first-order method), or by Newton's method (second-order). This way, gradient descent for any machine learning algorithm can be optimized.