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Gradient-based Hyperparameter Optimization through Reversible Learning

Dougal Maclaurin, David Duvenaud, Ryan P. Adams

2015 · arXiv

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Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure. These gradients allow us to optimize thousands of hyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures. We compute hyperparameter gradients by exactly reversing the dynamics of stochastic gradient descent with momentum.

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gwern
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No, it's been done. For example, "Gradient-based Hyperparameter Optimization through Reversible Learning" https://arxiv.org/abs/1502.03492 , Maclaurin et al 2015 (one of their cites). The idea is pretty obvious: of course you'd like to learn the hyperparameters like they were any other parameter. But that's easier said than done. The problem is that, well, to backpropagate through a hyperparameter, you would need to, say, track how it affects every iteration throughout the entire training run, rather than simply tracking one parameter through a single iteration on a single datapoint. And it's difficult enough to do gradient descent on a single hyperparameter, so it hardly…
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helps to start talking about doing entire stacks! If you can't really do one, doing ad infinitum probably isn't going to work well either. If you look at their experiment, they're doing a 1 hidden-layer FC NN on MNIST. (Honestly, I'm a little surprised that stacking hyperparams works even on that small a problem.)

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