SPSA
class SPSA(max_trials=1000, save_steps=1, last_avg=1, c0=0.6283185307179586, c1=0.1, c2=0.602, c3=0.101, c4=0, skip_calibration=False)
Simultaneous Perturbation Stochastic Approximation (SPSA) optimizer.
SPSA 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.
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.
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 includes a calibration phase, which requires additional functional evaluations.
For further details, please refer to https://arxiv.org/pdf/1704.05018v2.pdf#section*.11 (Supplementary information Section IV.)
Parameters
- max_trials (
int) – Maximum number of iterations to perform. - save_steps (
int) – Save intermediate info every save_steps step. It has a min. value of 1. - last_avg (
int) – Averaged parameters over the last_avg iterations. If last_avg = 1, only the last iteration is considered. It has a min. value of 1. - c0 (
float) – The initial a. Step size to update parameters. - c1 (
float) – The initial c. The step size used to approximate gradient. - c2 (
float) – The alpha in the paper, and it is used to adjust a (c0) at each iteration. - c3 (
float) – The gamma in the paper, and it is used to adjust c (c1) at each iteration. - c4 (
float) – The parameter used to control a as well. - skip_calibration (
float) – Skip calibration and use provided c(s) as is.
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
Methods
get_support_level
SPSA.get_support_level()
return support level dictionary
gradient_num_diff
static SPSA.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
optimize
SPSA.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
SPSA.print_options()
Print algorithm-specific options.
set_max_evals_grouped
SPSA.set_max_evals_grouped(limit)
Set max evals grouped
set_options
SPSA.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 SPSA.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