GradientDescent
class qiskit.algorithms.optimizers.GradientDescent(maxiter=100, learning_rate=0.01, tol=1e-07, callback=None, perturbation=None)
Bases: SteppableOptimizer
The gradient descent minimization routine.
For a function and an initial point , the standard (or “vanilla”) gradient descent method is an iterative scheme to find the minimum of by updating the parameters in the direction of the negative gradient of
for a small learning rate .
You can either provide the analytic gradient as jac
in the minimize()
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.
from qiskit.algorithms.optimizers import GradientDescent
def f(x):
return (np.linalg.norm(x) - 1) ** 2
initial_point = np.array([1, 0.5, -0.2])
optimizer = GradientDescent(maxiter=100)
result = optimizer.minimize(fun=fun, x0=initial_point)
print(f"Found minimum {result.x} at a value"
"of {result.fun} using {result.nfev} evaluations.")
An example where the learning rate is an iterator and we supply the analytic gradient. Note how much faster this convergences (i.e. less nfev
) compared to the previous example.
from qiskit.algorithms.optimizers import GradientDescent
def learning_rate():
power = 0.6
constant_coeff = 0.1
def powerlaw():
n = 0
while True:
yield constant_coeff * (n ** power)
n += 1
return powerlaw()
def f(x):
return (np.linalg.norm(x) - 1) ** 2
def grad_f(x):
return 2 * (np.linalg.norm(x) - 1) * x / np.linalg.norm(x)
initial_point = np.array([1, 0.5, -0.2])
optimizer = GradientDescent(maxiter=100, learning_rate=learning_rate)
result = optimizer.minimize(fun=fun, jac=grad_f, x0=initial_point)
print(f"Found minimum {result.x} at a value"
"of {result.fun} using {result.nfev} evaluations.")
An other example where the evaluation of the function has a chance of failing. The user, with specific knowledge about his function can catch this errors and handle them before passing the result to the optimizer.
import random import numpy as np from qiskit.algorithms.optimizers import GradientDescent def objective(x): if random.choice([True, False]): return None else: return (np.linalg.norm(x) - 1) ** 2 def grad(x): if random.choice([True, False]): return None else: return 2 * (np.linalg.norm(x) - 1) * x / np.linalg.norm(x) initial_point = np.random.normal(0, 1, size=(100,)) optimizer = GradientDescent(maxiter=20) optimizer.start(x0=initial_point, fun=objective, jac=grad) while optimizer.continue_condition(): ask_data = optimizer.ask() evaluated_gradient = None while evaluated_gradient is None: evaluated_gradient = grad(ask_data.x_center) optimizer.state.njev += 1 optmizer.state.nit += 1 tell_data = TellData(eval_jac=evaluated_gradient) optimizer.tell(ask_data=ask_data, tell_data=tell_data) result = optimizer.create_result()
Users that aren’t dealing with complicated functions and who are more familiar with step by step optimization algorithms can use the step()
method which wraps the ask()
and tell()
methods. In the same spirit the method minimize()
will optimize the function and return the result.
To see other libraries that use this interface one can visit: https://optuna.readthedocs.io/en/stable/tutorial/20_recipes/009_ask_and_tell.html
Parameters
- maxiter (int) – The maximum number of iterations.
- learning_rate (float |list[float] | np.ndarray | Callable[[], Generator[float, None, None]]) – A constant, list, array or factory of generators 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 has converged.
- perturbation (float | None) – If no gradient is passed to
minimize()
the gradient is approximated with a forward finite difference scheme withperturbation
perturbation in both directions (defaults to 1e-2 if required). Ignored when we have an explicit function for the gradient.
Raises
ValueError – If learning_rate
is an array and its length is less than maxiter
.
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
perturbation
Returns the perturbation.
This is the perturbation used in the finite difference gradient approximation.
setting
Return setting
settings
state
Return the current state of the optimizer.
tol
Returns the tolerance of the optimizer.
Any step with smaller stepsize than this value will stop the optimization.
Methods
ask
ask()
Returns an object with the data needed to evaluate the gradient.
If this object contains a gradient function the gradient can be evaluated directly. Otherwise approximate it with a finite difference scheme.
Return type
continue_condition
continue_condition()
Condition that indicates the optimization process should come to an end.
When the stepsize is smaller than the tolerance, the optimization process is considered finished.
Returns
True
if the optimization process should continue, False
otherwise.
Return type
create_result
create_result()
Creates a result of the optimization process.
This result contains the best point, the best function value, the number of function/gradient evaluations and the number of iterations.
Returns
The result of the optimization process.
Return type
evaluate
evaluate(ask_data)
Evaluates the gradient.
It does so either by evaluating an analytic gradient or by approximating it with a finite difference scheme. It will either add 1
to the number of gradient evaluations or add N+1
to the number of function evaluations (Where N is the dimension of the gradient).
Parameters
ask_data (AskData) – It contains the point where the gradient is to be evaluated and the gradient function or, in its absence, the objective function to perform a finite difference approximation.
Returns
The data containing the gradient evaluation.
Return type
get_support_level
get_support_level()
Get the support level dictionary.
gradient_num_diff
static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=None)
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, defaults to 1 (i.e. no batching).
Returns
the gradient computed
Return type
grad
minimize
minimize(fun, x0, jac=None, bounds=None)
Minimizes the function.
For well behaved functions the user can call this method to minimize a function. If the user wants more control on how to evaluate the function a custom loop can be created using ask()
and tell()
and evaluating the function manually.
Parameters
- fun (Callable[[POINT], float]) – Function to minimize.
- x0 (POINT) – Initial point.
- jac (Callable[[POINT], POINT] | None) – Function to compute the gradient.
- bounds (list[tuple[float, float]] | None) – Bounds of the search space.
Returns
Object containing the result of the optimization.
Return type
print_options
print_options()
Print algorithm-specific options.
set_max_evals_grouped
set_max_evals_grouped(limit)
Set max evals grouped
set_options
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.
start
start(fun, x0, jac=None, bounds=None)
Populates the state of the optimizer with the data provided and sets all the counters to 0.
Parameters
step
step()
Performs one step in the optimization process.
This method composes ask()
, evaluate()
, and tell()
to make a “step” in the optimization process.
tell
tell(ask_data, tell_data)
Updates x
by an amount proportional to the learning rate and value of the gradient at that point.
Parameters
- ask_data (AskData) – The data used to evaluate the function.
- tell_data (TellData) – The data from the function evaluation.
Raises
ValueError – If the gradient passed doesn’t have the right dimension.
wrap_function
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