  Deep learning methods achieve state-of-the-art performance in many
application scenarios. Yet, these methods require a significant amount of
hyperparameters tuning in order to achieve the best results. In particular,
tuning the learning rates in the stochastic optimization process is still one
of the main bottlenecks. In this paper, we propose a new stochastic gradient
descent procedure for deep networks that does not require any learning rate
setting. Contrary to previous methods, we do not adapt the learning rates nor
we make use of the assumed curvature of the objective function. Instead, we
reduce the optimization process to a game of betting on a coin and propose a
learning-rate-free optimal algorithm for this scenario. Theoretical convergence
is proven for convex and quasi-convex functions and empirical evidence shows
the advantage of our algorithm over popular stochastic gradient algorithms.
