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I am trying to optimize sklearn.linear_model.SGDRegressor, and I was wondering if people could point me in which direction I should try to optimize? Personal experience and literature are both welcome.

I think it would be much better if there is kind of a ranking in which way to search; should I start with finding a good alpha, or with a learning rate? Do you also have to do back checks at some point? What is the common way of searching this specific (or other sklearn/machine learning related) multivariate space? How dependent are these parameters on each other?

I understand this matters per situation, but how to do this kind of optimizing in a smarter way than level wise search?

I'm also never so sure when changing anything could have an effect on these paramaters. Basically if I would take a smaller sample, then I have no idea how solid the "optimal" values I found before, are.

E.g. some possible parameters to tune:

loss : ‘squared_loss’, ‘huber’, ‘epsilon_insensitive’, or        
       ‘squared_epsilon_insensitive’
alpha : float
l1_ratio: float between 0 (L2) and 1 (L1)
epsilon: float
learning_rate : optional
eta0 : double, optional
power_t : double, optional
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Leon Bottou's webpage has some good references on how to use SGD wisely(here is a link that you may find useful).

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There's a few options.

One is to search these hyper-parameters randomly then pick the one with the best cross-validation. I tend to run small experiments, record my results and then narrow the parameters. RandomizedSearchCV is a good starting point.

After getting a decent estimate of good hyperparameters, with some modules, you can set the pass the argument, verbosity=9, then look at the output at each iteration. Learning_rate, epsilon, eta0, n_iters, and power_t are influenced by one another. It's even more important for tuning Gradient Boosting. Personally I like this approach because I've been too lazy to throw down some code for the next paragraph. I also like the fast iteration associated with it. I can tune a model close to real-time, and stay in the feedback loop.

If you're willing to wade in undocumented water, then you can try to optimize over the hyperparameters with a Tree of Parzen Estimators, which has been shown in some cases to give a performance boost over Gaussian Process Confidence Bound methods but not in all. These are probably a much better approach, but their evaluation is time-consuming.

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