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 $f$

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

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.

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.

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

GradientDescent.get_support_level()

Get the support level dictionary.

gradient_num_diff

static GradientDescent.gradient_num_diff(x_center, f, epsilon, max_evals_grouped=1)

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) – the epsilon used in the numeric differentiation.
max_evals_grouped (int) – max evals grouped

Returns

the gradient computed

Return type

grad

minimize

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

Minimize the scalar function.

Parameters

fun (Callable[[Union[float, ndarray]], float]) – The scalar function to minimize.
x0 (Union[float, ndarray]) – The initial point for the minimization.
jac (Optional[Callable[[Union[float, ndarray]], Union[float, ndarray]]]) – The gradient of the scalar function fun.
bounds (Optional[List[Tuple[float, float]]]) – Bounds for the variables of fun. This argument might be ignored if the optimizer does not support bounds.

Return type

OptimizerResult

Returns

The result of the optimization, containing e.g. the result as attribute x.

optimize

GradientDescent.optimize(num_vars, objective_function, gradient_function=None, variable_bounds=None, initial_point=None)

Perform optimization.

Parameters

num_vars (int) – Number of parameters to be optimized.
objective_function (callable) – A function that computes the objective function.
gradient_function (callable) – A function that computes the gradient of the objective function, or None if not available.
variable_bounds (list[(float, float)]) – List of variable bounds, given as pairs (lower, upper). None means unbounded.
initial_point (numpy.ndarray[float]) – Initial point.

Returns

point, value, nfev

point: is a 1D numpy.ndarray[float] containing the solution value: is a float with the objective function value nfev: number of objective function calls made if available or None

Raises

ValueError – invalid input

print_options

GradientDescent.print_options()

Print algorithm-specific options.

set_max_evals_grouped

GradientDescent.set_max_evals_grouped(limit)

Set max evals grouped

set_options

GradientDescent.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) – options, given as name=value.

wrap_function

static GradientDescent.wrap_function(function, args)

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

Parameters

function (func) – the target function
args (tuple) – the args to be injected

Returns

wrapper

Return type

function_wrapper

Attributes

bounds_support_level

Returns bounds support level

gradient_support_level

Returns gradient 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_gradient_ignored

Returns is gradient ignored

is_gradient_required

Returns is gradient required

is_gradient_supported

Returns is gradient 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

setting

Return setting

settings

Return type

Dict[str, Any]

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