# qiskit.algorithms.optimizers.SPSA¶

class SPSA(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)[código fonte]

Simultaneous Perturbation Stochastic Approximation (SPSA) optimizer.

SPSA [1] is an algorithmic method for optimizing systems with multiple unknown parameters. As an optimization method, it is appropriately suited to large-scale population models, adaptive modeling, and simulation optimization.

Ver também

Many examples are presented at the SPSA Web site.

SPSA is a descent method capable of finding global minima, sharing this property with other methods as simulated annealing. Its main feature is the gradient approximation, which requires only two measurements of the objective function, regardless of the dimension of the optimization problem.

Nota

SPSA can be used in the presence of noise, and it is therefore indicated in situations involving measurement uncertainty on a quantum computation when finding a minimum. If you are executing a variational algorithm using a Quantum ASseMbly Language (QASM) simulator or a real device, SPSA would be the most recommended choice among the optimizers provided here.

The optimization process can includes a calibration phase if neither the learning_rate nor perturbation is provided, which requires additional functional evaluations. (Note that either both or none must be set.) For further details on the automatic calibration, please refer to the supplementary information section IV. of [2].

Referências

[1]: J. C. Spall (1998). An Overview of the Simultaneous Perturbation Method for Efficient Optimization, Johns Hopkins APL Technical Digest, 19(4), 482–492. Online.

[2]: A. Kandala et al. (2017). Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets. Nature 549, pages242–246(2017). arXiv:1704.05018v2

Parâmetros
• 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.

__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)[código fonte]
Parâmetros
• 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.

Methods

 __init__([maxiter, blocking, …]) type maxiter int calibrate(loss, initial_point[, c, …]) Calibrate SPSA parameters with a powerseries as learning rate and perturbation coeffs. estimate_stddev(loss, initial_point[, avg]) Estimate the standard deviation of the loss function. 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
property bounds_support_level

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)[código fonte]

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

The powerseries are:

$a_k = \frac{a}{(A + k + 1)^\alpha}, c_k = \frac{c}{(k + 1)^\gamma}$
Parâmetros
• 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).

Retorna

A tuple of powerseries generators, the first one for the

learning rate and the second one for the perturbation.

Tipo de retorno

tuple(generator, generator)

static estimate_stddev(loss, initial_point, avg=25)[código fonte]

Estimate the standard deviation of the loss function.

Tipo de retorno

float

get_support_level()[código fonte]

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.

Parâmetros
• 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

Retorna

Tipo de retorno

property 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

property is_gradient_required

property 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)[código fonte]

Perform optimization.

Parâmetros
• 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.

Retorna

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

Levanta

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.

Parâmetros

kwargs (dict) – options, given as name=value.

property setting

Return setting

static wrap_function(function, args)

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

Parâmetros
• function (func) – the target function

• args (tuple) – the args to be injected

Retorna

wrapper

Tipo de retorno

function_wrapper