# qiskit.algorithms.optimizers.GradientDescent¶

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

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.

__init__(maxiter=100, learning_rate=0.01, tol=1e-07, callback=None, perturbation=None)[source]
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

 __init__([maxiter, learning_rate, tol, …]) type maxiter int Get the support level dictionary. gradient_num_diff(x_center, f, epsilon[, …]) We compute the gradient with the numeric differentiation in the parallel way, around the point x_center. optimize(num_vars, objective_function[, …]) Perform optimization. Print algorithm-specific options. Set max evals grouped set_options(**kwargs) Sets or updates values in the options dictionary. wrap_function(function, args) Wrap the function to implicitly inject the args at the call of the function.

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 The optimizer settings in a dictionary format.
property bounds_support_level

Returns bounds support level

get_support_level()[source]

Get the support level dictionary.

static 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

property gradient_support_level

Returns gradient support level

property initial_point_support_level

Returns initial point support level

property is_bounds_ignored

Returns is bounds ignored

property is_bounds_required

Returns is bounds required

property is_bounds_supported

Returns is bounds supported

property is_gradient_ignored

Returns is gradient ignored

property is_gradient_required

Returns is gradient required

property is_gradient_supported

Returns is gradient supported

property is_initial_point_ignored

Returns is initial point ignored

property is_initial_point_required

Returns is initial point required

property is_initial_point_supported

Returns is initial point supported

optimize(num_vars, objective_function, gradient_function=None, variable_bounds=None, initial_point=None)[source]

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()

Print algorithm-specific options.

set_max_evals_grouped(limit)

Set max evals grouped

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.

property setting

Return setting

property settings

The optimizer settings in a dictionary format.

The settings can for instance be used for JSON-serialization (if all settings are serializable, which e.g. doesn’t hold per default for callables), such that the optimizer object can be reconstructed as

settings = optimizer.settings
# JSON serialize and send to another server
optimizer = OptimizerClass(**settings)

Return type

Dict[str, Any]

static 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