GradientDescent

GradientDescent(maxiter=100, learning_rate=0.01, tol=1e-07, callback=None, perturbation=None)

Bases: qiskit.algorithms.optimizers.steppable_optimizer.SteppableOptimizer

The gradient descent minimization routine.

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 $f$

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])
 
optimizer = GradientDescent(maxiter=100)
 
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
 
def grad_f(x):
    return 2 * (np.linalg.norm(x) - 1) * x / np.linalg.norm(x)
 
initial_point = np.array([1, 0.5, -0.2])
 
optimizer = GradientDescent(maxiter=100, learning_rate=learning_rate)
result = optimizer.minimize(fun=fun, jac=grad_f, x0=initial_point)
 
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
from qiskit.algorithms.optimizers import GradientDescent
 
def objective(x):
    if random.choice([True, False]):
        return None
    else:
        return (np.linalg.norm(x) - 1) ** 2
 
def grad(x):
    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,))
 
optimizer = GradientDescent(maxiter=20)
optimizer.start(x0=initial_point, fun=objective, jac=grad)
 
while optimizer.continue_condition():
    ask_data = optimizer.ask()
    evaluated_gradient = None
 
    while evaluated_gradient is None:
        evaluated_gradient = grad(ask_data.x_center)
        optimizer.state.njev += 1
 
    optmizer.state.nit += 1
 
    tell_data = TellData(eval_jac=evaluated_gradient)
    optimizer.tell(ask_data=ask_data, tell_data=tell_data)
 
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

• maxiter (int) – The maximum number of iterations.
• learning_rate (Union[float, List[float], ndarray, Callable[[], Iterator]]) – A constant, list, array or factory of generators yielding learning rates for the parameter updates. See the docstring for an example.
• tol (float) – If the norm of the parameter update is smaller than this threshold, the optimizer has converged.
• perturbation (Optional[float]) – If no gradient is passed to minimize() the gradient is approximated with a forward finite difference scheme with perturbation perturbation in both directions (defaults to 1e-2 if required). Ignored when we have an explicit function for the gradient.

Raises

ValueError – If learning_rate is an array and its lenght is less than maxiter.

Methods

ask

continue_condition

create_result

evaluate

get_support_level

gradient_num_diff

minimize

print_options

set_max_evals_grouped

set_options

start

step

tell

wrap_function

Attributes

bounds_support_level

gradient_support_level

initial_point_support_level

is_bounds_ignored

is_bounds_required

is_bounds_supported

is_gradient_ignored

is_gradient_required

is_gradient_supported

is_initial_point_ignored

is_initial_point_required

is_initial_point_supported

perturbation

setting

settings

state

tol