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We introduce a general method for improving the convergence rate ofgradient-based optimizers that is easy to implement and works well in practice.We demonstrate the effectiveness of the method in a range of optimizationproblems by applying it to stochastic gradient descent, stochastic gradientdescent with Nesterov momentum, and Adam, showing that it significantly reducesthe need for the manual tuning of the initial learning rate for these commonlyused algorithms. Our method works by dynamically updating the learning rateduring optimization using the gradient with respect to the learning rate of theupdate rule itself. Computing this "hypergradient" needs little additionalcomputation, requires only one extra copy of the original gradient to be storedin memory, and relies upon nothing more than what is provided by reverse-modeautomatic differentiation.

Online Learning Rate Adaptation with Hypergradient Descent