ELRA: Exponential learning rate adaption gradient descent optimization
  method
Alexander Kleinsorge Stefan Kupper Alexander Fauck Felix Rothe
We present a novel, fast (exponential rate adaption), ab initio
(hyper-parameter-free) gradient based optimizer algorithm. The main idea of the
method is to adapt the learning rate $\alpha$ by situational awareness, mainly
striving for orthogonal neighboring gradients. The method has a high success
and fast convergence rate and does not rely on hand-tuned parameters giving it
greater universality. It can be applied to problems of any dimensions n and
scales only linearly (of order O(n)) with the dimension of the problem. It
optimizes convex and non-convex continuous landscapes providing some kind of
gradient. In contrast to the Ada-family (AdaGrad, AdaMax, AdaDelta, Adam, etc.)
the method is rotation invariant: optimization path and performance are
independent of coordinate choices. The impressive performance is demonstrated
by extensive experiments on the MNIST benchmark data-set against
state-of-the-art optimizers. We name this new class of optimizers after its
core idea Exponential Learning Rate Adaption - ELRA. We present it in two
variants c2min and p2min with slightly different control. The authors strongly
believe that ELRA will open a completely new research direction for gradient
descent optimize.