# Gradient descent revisited via an adaptive online learning rate

2018 Feb 04One of the most misunderstood concepts and the reason that a lot of cash is spent in Machine Learning as a Service (MLaaS) due a lack of optimization in this parameter that is responsible to control the convergence. Gradient descent revisited via an adaptive online learning rate

**Abstract**: 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 η is not fixed. Instead, we learn η 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.

**Conclusion:** In this paper, we have built a new way to learn the learning rate at each step using finite differences on the loss. We have tested it on a variety of convex and non-convex optimization tasks. Based on our results, we believe that our method would be able to adapt a good learning rate at every iteration on convex problems. In the case of non-convex problems, we repeatedly observed faster training in the first few epochs. However, our adaptive model seems more inclined to overfit the training data, even though its test accuracy is always comparable to standard SGD performance, if not slightly better. Hence we believe that in neural network architectures, our model can be used initially for pretraining for a few epochs, and then continue with any other standard optimization technique to lead to faster convergence and be computationally more efficient, and perhaps reach a new highest accuracy on the given problem. Moreover, the learning rate that our algorithm converges to suggests an ideal learning rate for the given training task. One could use our method to tune the learning rate of a standard neural network (using Adam for instance), giving a more precise value than with line-search or random search.