Online Learning Rate Adaptation with Hypergradient Descent
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We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We analyze the effectiveness of the method by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it improves upon these commonly used algorithms on a range of optimization problems; in particular the kinds of objective functions that arise frequently in deep neural network training. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.
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