  In modern supervised learning, many deep neural networks are able to
interpolate the data: the empirical loss can be driven to near zero on all
samples simultaneously. In this work, we explicitly exploit this interpolation
property for the design of a new optimization algorithm for deep learning,
which we term Adaptive Learning-rates for Interpolation with Gradients (ALI-G).
ALI-G retains the two main advantages of Stochastic Gradient Descent (SGD),
which are (i) a low computational cost per iteration and (ii) good
generalization performance in practice. At each iteration, ALI-G exploits the
interpolation property to compute an adaptive learning-rate in closed form. In
addition, ALI-G clips the learning-rate to a maximal value, which we prove to
be helpful for non-convex problems. Crucially, in contrast to the learning-rate
of SGD, the maximal learning-rate of ALI-G does not require a decay schedule,
which makes it considerably easier to tune. We provide convergence guarantees
of ALI-G in various stochastic settings. Notably, we tackle the realistic case
where the interpolation property is satisfied up to some tolerance. We provide
experiments on a variety of architectures and tasks: (i) learning a
differentiable neural computer; (ii) training a wide residual network on the
SVHN data set; (iii) training a Bi-LSTM on the SNLI data set; and (iv) training
wide residual networks and densely connected networks on the CIFAR data sets.
ALI-G produces state-of-the-art results among adaptive methods, and even yields
comparable performance with SGD, which requires manually tuned learning-rate
schedules. Furthermore, ALI-G is simple to implement in any standard deep
learning framework and can be used as a drop-in replacement in existing code.
