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Declarative Machine Learning
#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
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# to you under the Apache License, Version 2.0 (the
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#-------------------------------------------------------------
/*
* RMSprop optimizer.
*/
update = function(matrix[double] X, matrix[double] dX, double lr, double decay_rate,
double epsilon, matrix[double] cache)
return (matrix[double] X, matrix[double] cache) {
/*
* Performs an RMSprop update.
*
* This is an adaptive learning rate optimizer that can be viewed
* as an adjustment of the Adagrad method to use a moving average
* of the sum of squared gradients in order to improve convergence.
*
* Reference:
* - Neural Networks for Machine Learning, Lecture 6a, Hinton,
* slide 29.
* - http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
*
* Inputs:
* - X: Parameters to update, of shape (any, any).
* - dX: Gradient wrt `X` of a loss function being optimized, of
* same shape as `X`.
* - lr: Learning rate.
* - decay_rate: Term controlling the rate of the moving average.
* Typical values are in the range of [0.9, 0.999].
* - epsilon: Smoothing term to avoid divide by zero errors.
* Typical values are in the range of [1e-8, 1e-4].
* - cache: State that maintains the moving average of the squared
* gradients, of same shape as `X`.
*
* Outputs:
* - X: Updated parameters `X`, of same shape as input `X`.
* - cache: Updated state that maintains the moving average of the
* squared gradients, of same shape as `X`.
*/
cache = decay_rate*cache + (1-decay_rate)*dX^2
X = X - (lr * dX / (sqrt(cache)+epsilon))
}
init = function(matrix[double] X)
return (matrix[double] cache) {
/*
* Initialize the state for this optimizer.
*
* Note: This is just a convenience function, and state
* may be initialized manually if needed.
*
* Inputs:
* - X: Parameters to update, of shape (any, any).
*
* Outputs:
* - cache: State that maintains the moving average of the squared
* gradients, of same shape as `X`.
*/
cache = matrix(0, rows=nrow(X), cols=ncol(X))
}