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Declarative Machine Learning
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/*
* Adagrad optimizer.
*/
update = function(matrix[double] X, matrix[double] dX, double lr, double epsilon,
matrix[double] cache)
return (matrix[double] X, matrix[double] cache) {
/*
* Performs an Adagrad update.
*
* This is an adaptive learning rate optimizer that maintains the
* sum of squared gradients to automatically adjust the effective
* learning rate.
*
* Reference:
* - Adaptive Subgradient Methods for Online Learning and Stochastic
* Optimization, Duchi et al.
* - http://jmlr.org/papers/v12/duchi11a.html
*
* 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.
* - epsilon: Smoothing term to avoid divide by zero errors.
* Typical values are in the range of [1e-8, 1e-4].
* - cache: State that maintains per-parameter sum of squared
* gradients, of same shape as `X`.
*
* Outputs:
* - X: Updated parameters `X`, of same shape as input `X`.
* - cache: State that maintains per-parameter sum of squared
* gradients, of same shape as `X`.
*/
cache = cache + 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 per-parameter sum of squared
* gradients, of same shape as `X`.
*/
cache = matrix(0, rows=nrow(X), cols=ncol(X))
}