qiskit.algorithms.optimizers.SPSA

__init__(maxiter=100, blocking=False, allowed_increase=None, trust_region=False, learning_rate=None, perturbation=None, last_avg=1, resamplings=1, perturbation_dims=None, callback=None)

Parameters

• maxiter (int) – The maximum number of iterations.
• blocking (bool) – If True, only accepts updates that improve the loss (minus some allowed increase, see next argument).
• allowed_increase (Optional[float]) – If blocking is True, this sets by how much the loss can increase and still be accepted. If None, calibrated automatically to be twice the standard deviation of the loss function.
• trust_region (bool) – If True, restricts norm of the random direction to be $\leq 1$.
• learning_rate (Union[float, Callable[[], Iterator], None]) – A generator yielding learning rates for the parameter updates, $a_k$. If set, also perturbation must be provided.
• perturbation (Union[float, Callable[[], Iterator], None]) – A generator yielding the perturbation magnitudes $c_k$. If set, also learning_rate must be provided.
• last_avg (int) – Return the average of the last_avg parameters instead of just the last parameter values.
• resamplings (Union[int, Dict[int, int]]) – The number of times the gradient is sampled using a random direction to construct a gradient estimate. Per default the gradient is estimated using only one random direction. If an integer, all iterations use the same number of resamplings. If a dictionary, this is interpreted as {iteration: number of resamplings per iteration}.
• perturbation_dims (Optional[int]) – The number of perturbed dimensions. Per default, all dimensions are perturbed, but a smaller, fixed number can be perturbed. If set, the perturbed dimensions are chosen uniformly at random.
• callback (Optional[Callable[[int, ndarray, float, float, bool], None]]) – A callback function passed information in each iteration step. The information is, in this order: the number of function evaluations, the parameters, the function value, the stepsize, whether the step was accepted.

Returns bounds support level

static calibrate(loss, initial_point, c=0.2, stability_constant=0, target_magnitude=None, alpha=0.602, gamma=0.101, modelspace=False)

Calibrate SPSA parameters with a powerseries as learning rate and perturbation coeffs.

The powerseries are:

Parameters

• loss (Callable[[ndarray], float]) – The loss function.
• initial_point (ndarray) – The initial guess of the iteration.
• c (float) – The initial perturbation magnitude.
• stability_constant (float) – The value of A.
• target_magnitude (Optional[float]) – The target magnitude for the first update step, defaults to $2\pi / 10$.
• alpha (float) – The exponent of the learning rate powerseries.
• gamma (float) – The exponent of the perturbation powerseries.
• modelspace (bool) – Whether the target magnitude is the difference of parameter values or function values (= model space).

Returns

A tuple of powerseries generators, the first one for the

learning rate and the second one for the perturbation.

Return type

tuple(generator, generator)

static estimate_stddev(loss, initial_point, avg=25)

Estimate the standard deviation of the loss function.

Return type

float

get_support_level()

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

Returns gradient support level

Returns initial point support level

Returns is bounds ignored

Returns is bounds required

Returns is bounds supported

Returns is gradient ignored

Returns is gradient required

Returns is gradient supported

Returns is initial point ignored

Returns is initial point required

Returns is initial point supported

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()

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.

Return setting

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