qml.RMSPropOptimizer

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

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)

Methods

apply_grad(grad, args)	Update the variables args to take a single optimization step.
compute_grad(objective_fn, args, kwargs[, …])	Compute gradient of the objective function at the given point and return it along with the objective function forward pass (if available).
reset()	Reset optimizer by erasing memory of past steps.
step(objective_fn, *args[, grad_fn])	Update trainable arguments with one step of the optimizer.
step_and_cost(objective_fn, *args[, grad_fn])	Update trainable arguments with one step of the optimizer and return the corresponding objective function value prior to the step.

apply_grad(grad, args)

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

Parameters

• grad (tuple [array]) – the gradient of the objective function at point \(x^{(t)}\): \(\nabla f(x^{(t)})\).

• args (tuple) – the current value of the variables \(x^{(t)}\).

Returns

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

Return type

list [array]

static compute_grad(objective_fn, args, kwargs, grad_fn=None)

Compute gradient of the objective function at the given point and return it along with the objective function forward pass (if available).

Parameters

• objective_fn (function) – the objective function for optimization

• args (tuple) – tuple of NumPy arrays containing the current parameters for the objection function

• kwargs (dict) – keyword arguments for the objective function

• grad_fn (function) – optional gradient function of the objective function with respect to the variables args. If None, the gradient function is computed automatically. Must return the same shape of tuple [array] as the autograd derivative.

Returns

NumPy array containing the gradient \(\nabla f(x^{(t)})\) and the objective function output. If grad_fn is provided, the objective function will not be evaluted and instead None will be returned.

Return type

tuple (array)

reset()

Reset optimizer by erasing memory of past steps.

step(objective_fn, *args, grad_fn=None, **kwargs)

Update trainable arguments with one step of the optimizer.

Parameters

• objective_fn (function) – the objective function for optimization

• *args – Variable length argument list for objective function

• grad_fn (function) – optional gradient function of the objective function with respect to the variables x. If None, the gradient function is computed automatically. Must return a tuple[array] with the same number of elements as *args. Each array of the tuple should have the same shape as the corresponding argument.

• **kwargs – variable length of keyword arguments for the objective function

Returns

the new variable values \(x^{(t+1)}\). If single arg is provided, list [array] is replaced by array.

Return type

list [array]

step_and_cost(objective_fn, *args, grad_fn=None, **kwargs)

Update trainable arguments with one step of the optimizer and return the corresponding objective function value prior to the step.

Parameters

• objective_fn (function) – the objective function for optimization

• *args – variable length argument list for objective function

• grad_fn (function) – optional gradient function of the objective function with respect to the variables *args. If None, the gradient function is computed automatically. Must return a tuple[array] with the same number of elements as *args. Each array of the tuple should have the same shape as the corresponding argument.

• **kwargs – variable length of keyword arguments for the objective function

Returns

the new variable values \(x^{(t+1)}\) and the objective function output prior to the step. If single arg is provided, list [array] is replaced by array.

Return type

tuple[list [array], float]

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