GradientDescent

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

Bases: qiskit.algorithms.optimizers.optimizer.Optimizer

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 $\eta > 0$.

You can either provide the analytic gradient $\vec\nabla f$ as gradient_function in the optimize 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)
x_opt, fx_opt, nfevs = optimizer.optimize(initial_point.size,
                                          f,
                                          initial_point=initial_point)
 
print(f"Found minimum {x_opt} at a value of {fx_opt} using {nfevs} 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 nfevs) 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)
x_opt, fx_opt, nfevs = optimizer.optimize(initial_point.size,
                                          f,
                                          gradient_function=grad_f,
                                          initial_point=initial_point)
 
print(f"Found minimum {x_opt} at a value of {fx_opt} using {nfevs} evaluations.")

Parameters

• maxiter (int) – The maximum number of iterations.
• learning_rate (Union[float, Callable[[], Iterator]]) – A constant or generator 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 is converged.
• perturbation (Optional[float]) – If no gradient is passed to GradientDescent.optimize the gradient is approximated with a symmetric finite difference scheme with perturbation perturbation in both directions (defaults to 1e-2 if required). Ignored if a gradient callable is passed to GradientDescent.optimize.

Methods

get_support_level

gradient_num_diff

minimize

print_options

set_max_evals_grouped

set_options

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

setting

settings