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https://issues.apache.org/jira/browse/MADLIB-1210?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16501169#comment-16501169
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Jingyi Mei commented on MADLIB-1210:
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Spiked on default momentum value settings - we did group of experiments(with
MNIST data set) on different momentum values, with Nesterov True or False,
tried both minibatch and Stochastic, and also tuned learning rate. Please see
the attached pdf for result. [^MLP Momentum Default Value Experiments.pdf]
Generally, momentum = 0.9 with Nesterov=True works well. It may not be the best
comparing with some other values (like momentum=0.4 or momentum=0.5) combining
with different learning rate. However, it only applied to MNIST data set and
users can always specify different set of optimizer parameters. Thus we decided
to keep momentum = 0.9 and nesterov=True as default values.
> Add momentum methods to MLP
> ---------------------------
>
> Key: MADLIB-1210
> URL: https://issues.apache.org/jira/browse/MADLIB-1210
> Project: Apache MADlib
> Issue Type: New Feature
> Components: Module: Neural Networks
> Reporter: Frank McQuillan
> Priority: Major
> Fix For: v1.15
>
> Attachments: MLP Momentum Default Value Experiments.pdf, Momentum
> methods comparison.xlsx, momentum with MNIST dataset.pdf
>
>
> Story
> As a data scientist,
> I want to use momentum methods in MLP,
> so that I get significantly better convergence behavior.
> Details
> Adding momentum will get the MADlib MLP algorithm closer to state of the art.
> 1) Implement momentum term, default value ~0.9
> Ref [1]:
> "Momentum update is another approach that almost always enjoys better
> converge rates on deep networks."
> 2) Implement Nesterov momentum, default TRUE
> Ref [1]:
> "Nesterov Momentum is a slightly different version of the momentum update
> that has recently been gaining popularity. It enjoys stronger theoretical
> converge guarantees for convex functions and in practice it also consistently
> works slightly better than standard momentum."
> Ref [2]
> "Nesterov’s accelerated gradient (abbrv. NAG; Nesterov, 1983) is a
> first-order optimization method which is proven to have a better convergence
> rate guarantee than gradient descent for general convex functions with
> Lipshitz-continuous derivatives (O(1/T2) versus O(1/T))"
> Interface
> There are 2 new optimization params for momentum, which apply for both
> classification and regression:
> {code}
> 'learning_rate_init = <value>,
> learning_rate_policy = <value>,
> gamma = <value>,
> power = <value>,
> iterations_per_step = <value>,
> n_iterations = <value>,
> n_tries = <value>,
> lambda = <value>,
> tolerance = <value>,
> batch_size = <value>,
> n_epochs = <value>,
> momentum = <value>,
> nesterov= <value>'
> momentum
> FLOAT8, default: 0.9. Momentum can help accelerate learning and
> avoid local minima when using gradient descent. Value must be in the
> range 0 to 1, where 0 means no momentum.
> nesterov
> BOOLEAN, default: TRUE. Nesterov momentum can provide better results than
> using
> classical momentum alone, due to its look ahead characteristics.
> In classical momentum you first correct velocity and step with that
> velocity, whereas in Nesterov momentum you first step in the velocity
> direction then make a correction to the velocity vector based on
> new location.
> Nesterov momentum is only used when the 'momentum' parameter is > 0.
> {code}
> Open questions
> 1) Does momentum and Nesterov momentum work equally well with and without
> mini-batching?
> Is there any guidance we need to give to users on this?
> Acceptance
> [1] Compare the usefulness of momentum with and without Nesterov, and SGD
> (i.e., 3 comparisons). Use a 2D Rosenbrock function to compare in a similar
> way to test ref [100] in the comment further down, i.e., loss by iteration
> number. Maybe try a few different 2D slices (starting points)
> [2] Test with MNIST. Please generate characteristic curves of loss vs.
> iteration number, similar to what was done for Rosenbrock.
> [3] Report out momentum value and Nesterov in the output summary table.
> References
> [1] http://cs231n.github.io/neural-networks-3/#sgd
> [2] http://www.cs.utoronto.ca/~ilya/pubs/ilya_sutskever_phd_thesis.pdf, a
> link from previous source.
> [3]
> http://ruder.io/optimizing-gradient-descent/index.html#gradientdescentoptimizationalgorithms
> [4]
> http://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPClassifier.html
> [5] https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
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