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class qiskit.algorithms.optimizers.GradientDescent(maxiter=100, learning_rate=0.01, tol=1e-07, callback=None, perturbation=None)

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For a function $f$ and an initial point $\vec\theta_0$, the standard (or “vanilla”) gradient descent method is an iterative scheme to find the minimum $\vec\theta^*$ of $f$ by updating the parameters in the direction of the negative gradient of $f$

$\vec\theta_{n+1} = \vec\theta_{n} - \eta_n \vec\nabla f(\vec\theta_{n}),$

for a small learning rate $\eta_n > 0$.

You can either provide the analytic gradient $\vec\nabla f$ as jac in the minimize() method, or, if you do not provide it, use a finite difference approximation of the gradient. To adapt the size of the perturbation in the finite difference gradients, set the perturbation property in the initializer.

This optimizer supports a callback function. If provided in the initializer, the optimizer will call the callback in each iteration with the following information in this order: current number of function values, current parameters, current function value, norm of current gradient.

Examples

A minimum example that will use finite difference gradients with a default perturbation of 0.01 and a default learning rate of 0.01.

from qiskit.algorithms.optimizers import GradientDescent

def f(x):
return (np.linalg.norm(x) - 1) ** 2

initial_point = np.array([1, 0.5, -0.2])

result = optimizer.minimize(fun=fun, x0=initial_point)

print(f"Found minimum {result.x} at a value"
"of {result.fun} using {result.nfev} evaluations.")

An example where the learning rate is an iterator and we supply the analytic gradient. Note how much faster this convergences (i.e. less nfev) compared to the previous example.

from qiskit.algorithms.optimizers import GradientDescent

def learning_rate():
power = 0.6
constant_coeff = 0.1
def powerlaw():
n = 0
while True:
yield constant_coeff * (n ** power)
n += 1

return powerlaw()

def f(x):
return (np.linalg.norm(x) - 1) ** 2

return 2 * (np.linalg.norm(x) - 1) * x / np.linalg.norm(x)

initial_point = np.array([1, 0.5, -0.2])

print(f"Found minimum {result.x} at a value"
"of {result.fun} using {result.nfev} evaluations.")

An other example where the evaluation of the function has a chance of failing. The user, with specific knowledge about his function can catch this errors and handle them before passing the result to the optimizer.

import random
import numpy as np

def objective(x):
if random.choice([True, False]):
return None
else:
return (np.linalg.norm(x) - 1) ** 2

if random.choice([True, False]):
return None
else:
return 2 * (np.linalg.norm(x) - 1) * x / np.linalg.norm(x)

initial_point = np.random.normal(0, 1, size=(100,))

while optimizer.continue_condition():

optimizer.state.njev += 1

optmizer.state.nit += 1

result = optimizer.create_result()

Users that aren’t dealing with complicated functions and who are more familiar with step by step optimization algorithms can use the step() method which wraps the ask() and tell() methods. In the same spirit the method minimize() will optimize the function and return the result.

To see other libraries that use this interface one can visit: https://optuna.readthedocs.io/en/stable/tutorial/20_recipes/009_ask_and_tell.html(opens in a new tab)

Parameters

Raises

ValueError(opens in a new tab) – If learning_rate is an array and its length is less than maxiter.

Attributes

bounds_support_level

Returns bounds support level

initial_point_support_level

Returns initial point support level

is_bounds_ignored

Returns is bounds ignored

is_bounds_required

Returns is bounds required

is_bounds_supported

Returns is bounds supported

is_initial_point_ignored

Returns is initial point ignored

is_initial_point_required

Returns is initial point required

is_initial_point_supported

Returns is initial point supported

perturbation

Returns the perturbation.

This is the perturbation used in the finite difference gradient approximation.

Return setting

state

Return the current state of the optimizer.

tol

Returns the tolerance of the optimizer.

Any step with smaller stepsize than this value will stop the optimization.

Methods

ask()

Returns an object with the data needed to evaluate the gradient.

If this object contains a gradient function the gradient can be evaluated directly. Otherwise approximate it with a finite difference scheme.

Return type

continue_condition

continue_condition()

Condition that indicates the optimization process should come to an end.

When the stepsize is smaller than the tolerance, the optimization process is considered finished.

Returns

True if the optimization process should continue, False otherwise.

Return type

bool(opens in a new tab)

create_result

create_result()

Creates a result of the optimization process.

This result contains the best point, the best function value, the number of function/gradient evaluations and the number of iterations.

Returns

The result of the optimization process.

Return type

OptimizerResult

evaluate

evaluate(ask_data)

It does so either by evaluating an analytic gradient or by approximating it with a finite difference scheme. It will either add 1 to the number of gradient evaluations or add N+1 to the number of function evaluations (Where N is the dimension of the gradient).

Parameters

ask_data (AskData) – It contains the point where the gradient is to be evaluated and the gradient function or, in its absence, the objective function to perform a finite difference approximation.

Returns

The data containing the gradient evaluation.

Return type

TellData

get_support_level

get_support_level()

Get the support level dictionary.

static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=None)

We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.

Parameters

• x_center (ndarray) – point around which we compute the gradient
• f (func) – the function of which the gradient is to be computed.
• epsilon (float(opens in a new tab)) – the epsilon used in the numeric differentiation.
• max_evals_grouped (int(opens in a new tab)) – max evals grouped, defaults to 1 (i.e. no batching).

Returns

Return type

minimize

minimize(fun, x0, jac=None, bounds=None)

Minimizes the function.

For well behaved functions the user can call this method to minimize a function. If the user wants more control on how to evaluate the function a custom loop can be created using ask() and tell() and evaluating the function manually.

Parameters

Returns

Object containing the result of the optimization.

Return type

OptimizerResult

print_options()

Print algorithm-specific options.

set_max_evals_grouped

set_max_evals_grouped(limit)

Set max evals grouped

set_options

set_options(**kwargs)

Sets or updates values in the options dictionary.

The options dictionary may be used internally by a given optimizer to pass additional optional values for the underlying optimizer/optimization function used. The options dictionary may be initially populated with a set of key/values when the given optimizer is constructed.

Parameters

kwargs (dict(opens in a new tab)) – options, given as name=value.

start

start(fun, x0, jac=None, bounds=None)

Populates the state of the optimizer with the data provided and sets all the counters to 0.

Parameters

step

step()

Performs one step in the optimization process.

This method composes ask(), evaluate(), and tell() to make a “step” in the optimization process.

tell

tell(ask_data, tell_data)

Updates x by an amount proportional to the learning rate and value of the gradient at that point.

Parameters

• tell_data (TellData) – The data from the function evaluation.

Raises

ValueError(opens in a new tab) – If the gradient passed doesn’t have the right dimension.

wrap_function

static wrap_function(function, args)

Wrap the function to implicitly inject the args at the call of the function.

Parameters

Returns

wrapper

Return type

function_wrapper