qml.RMSPropOptimizer

class RMSPropOptimizer(stepsize=0.01, decay=0.9, eps=1e-08)[source]

Bases: pennylane.optimize.adagrad.AdagradOptimizer

Root mean squared propagation optimizer.

The root mean square progation optimizer is a modified Adagrad optimizer, with a decay of learning rate adaptation.

Extensions of the Adagrad optimization method generally start the sum \(a\) over past gradients in the denominator of the learning rate at a finite \(t'\) with \(0 < t' < t\), or decay past gradients to avoid an ever-decreasing learning rate.

Root Mean Square propagation is such an adaptation, where

\[a_i^{(t+1)} = \gamma a_i^{(t)} + (1-\gamma) (\partial_{x_i} f(x^{(t)}))^2.\]
Parameters
  • stepsize (float) – the user-defined hyperparameter \(\eta\) used in the Adagrad optmization

  • decay (float) – the learning rate decay \(\gamma\)

  • eps (float) – offset \(\epsilon\) added for numerical stability (see Adagrad)

apply_grad(grad, x)

Update the variables x to take a single optimization step.

compute_grad(objective_fn, x[, grad_fn])

Compute gradient of the objective_fn at the point x.

reset()

Reset optimizer by erasing memory of past steps.

step(objective_fn, x[, grad_fn])

Update x with one step of the optimizer.

update_stepsize(stepsize)

Update the initialized stepsize value \(\eta\).

apply_grad(grad, x)[source]

Update the variables x to take a single optimization step. Flattens and unflattens the inputs to maintain nested iterables as the parameters of the optimization.

Parameters
  • grad (array) – The gradient of the objective function at point \(x^{(t)}\): \(\nabla f(x^{(t)})\)

  • x (array) – the current value of the variables \(x^{(t)}\)

Returns

the new values \(x^{(t+1)}\)

Return type

array

static compute_grad(objective_fn, x, grad_fn=None)

Compute gradient of the objective_fn at the point x.

Parameters
  • objective_fn (function) – the objective function for optimization

  • x (array) – NumPy array containing the current values of the variables to be updated

  • grad_fn (function) – Optional gradient function of the objective function with respect to the variables x. If None, the gradient function is computed automatically.

Returns

NumPy array containing the gradient \(\nabla f(x^{(t)})\)

Return type

array

reset()

Reset optimizer by erasing memory of past steps.

step(objective_fn, x, grad_fn=None)

Update x with one step of the optimizer.

Parameters
  • objective_fn (function) – the objective function for optimization

  • x (array) – NumPy array containing the current values of the variables to be updated

  • grad_fn (function) – Optional gradient function of the objective function with respect to the variables x. If None, the gradient function is computed automatically.

Returns

the new variable values \(x^{(t+1)}\)

Return type

array

update_stepsize(stepsize)

Update the initialized stepsize value \(\eta\).

This allows for techniques such as learning rate scheduling.

Parameters

stepsize (float) – the user-defined hyperparameter \(\eta\)

Contents

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