qml.NesterovMomentumOptimizer

class NesterovMomentumOptimizer(stepsize=0.01, momentum=0.9)

Bases: pennylane.optimize.momentum.MomentumOptimizer

Gradient-descent optimizer with Nesterov momentum.

Nesterov Momentum works like the Momentum optimizer, but shifts the current input by the momentum term when computing the gradient of the objective function:

\[a^{(t+1)} = m a^{(t)} + \eta \nabla f(x^{(t)} - m a^{(t)}).\]

The user defined parameters are:

• \(\eta\): the step size

• \(m\): the momentum

Parameters

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

• momentum (float) – user-defined hyperparameter \(m\)

Methods

apply_grad(grad, args)	Update the trainable args to take a single optimization step.
compute_grad(objective_fn, args, kwargs[, …])	Compute gradient of the objective function at at the shifted point \((x - m\times\text{accumulation})\) 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.
update_stepsize(stepsize)	Update the initialized stepsize value \(\eta\).

apply_grad(grad, args)

Update the trainable 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]

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

Compute gradient of the objective function at at the shifted point \((x - m\times\text{accumulation})\) 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 values 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 x. If None, the gradient function is computed automatically. Must return the same shape of tuple [array] as the autograd derivative.

Returns

the 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]

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 \(\eta\)