[1705.07795] Training Deep Networks without Learning Rates Through Coin Betting
For all the algorithms, but COCOB, we select their learning rate as the one that gives the best training cost a posteriori using a very fine grid of values [[0.00001, 0.000025, 0.00005, 0.000075, 0.0001, 0.00025, 0.0005, 0.00075, 0.001, 0.0025, 0.005, 0.0075, 0.01, 0.02, 0.05, 0.075, 0.1]]

Abstract: 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.

‹Figure 2: Behaviour of COCOB (left) and gradient descent with various learning rates and same number of steps (center) in minimizing the function y = |x − 10|. (right) The effective learning rates of COCOB. Figures best viewed in colors. (The COCOB Algorithm)Figure 3: Training cost (cross-entropy) (left) and testing error rate (0/1 loss) (right) vs. the number epochs with two different architectures on MNIST, as indicated in the figure titles. The y-axis is logarithmic in the left plots. Figures best viewed in colors. (Empirical Results and Future Work)Figure 4: Training cost (cross-entropy) (left) and testing error rate (0/1 loss) (right) vs. the number epochs on CIFAR-10. The y-axis is logarithmic in the left plots. Figures best viewed in colors. (Empirical Results and Future Work)Figure 5: Training cost (left) and test cost (right) measured as average per-word perplexity vs. the number epochs on PTB word-level language modeling task. Figures best viewed in colors. (Empirical Results and Future Work)›