import pennylane as qml
from datetime import datetime
import time
[docs]def gradient_descent(
cost,
init_settings,
num_steps=150,
step_size=0.1,
sample_width=25,
grad_fn=None,
verbose=True,
interface="autograd",
optimizer=None,
optimizer_kwargs={},
):
"""Performs a numerical gradient descent optimization on the provided ``cost`` function.
The optimization is seeded with (random) ``init_settings`` which are then varied to
minimze the cost.
:param cost: The cost function to be minimized with gradient descent.
:type cost: function
:param init_settings: A valid input for the cost function.
:type init_settings: array-like[float]
:param num_steps: The number of gradient descent iterations, defaults to ``150``.
:type num_steps: int, optional
:param step_size: The learning rate for the gradient descent, defaults to ``0.1``.
:type step_size: float, optional
:param sample_width: The number of steps between "sampled" costs which are printed/returned
to user, defaults to ``25``.
:type sample_width: int, optional
:param grad_fn: A custom gradient function, default to ``None`` which applies the standard numerical gradient.
:type grad_fn: function, optional
:param verbose: If ``True``, progress is printed during the optimization, defaults to ``True``.
:type verbose: bool, optional
:param interface: Specifies the optimizer software either ``"autograd"`` or ``"tf"`` (TensorFlow).
:type interface: string, default ``"autograd``"
:param optimizer: Specifies the PennyLane optimizer to use. Default ``qml.GradientDescentOptimizer``.
Set to ``"adam"`` to use the ``qml.AdamOptimizer``, note that ``interface="autograd"`` must be set.
:type optimizer: String
:param optimizer_kwargs: Keyword arguments to pass to the specified optimizer.
:type optimizer_kwargs: Dict
:return: Data regarding the gradient descent optimization.
:rtype: dictionary, contains the following keys:
* **opt_score** (*float*) - The maximized reward ``-(min_cost)``.
* **opt_settings** (*array-like[float]*) - The setting for which the optimum is achieved.
* **scores** (*array[float]*) - The list of rewards sampled during the gradient descent.
* **samples** (*array[int]*) - A list containing the iteration for each sample.
* **settings_history** (*array[array-like]*) - A list of all settings found for each
intermediate step of gradient descent
* **datetime** (*string*) - The date and time in UTC when the optimization occurred.
* **step_times** (*list[float]*) - The time elapsed during each sampled optimization step.
* **step_size** (*float*) - The learning rate of the optimization.
.. warning::
The ``gradient_descent`` function minimizes the cost function, however, the general
use case within this project is to maximize the violation of a Bell inequality.
The maximization is assumed within ``gradient_descent`` and is applied by multiplying
the cost by (-1). This is an abuse of function naming and will be resolved in a future
commit by having ``gradient_descent`` return the minimized cost rather than the maximized
reward. The resolution is to wrap ``gradient_descent`` with a ``gradient_ascent`` function
which maximizes a reward function equivalent to ``-(cost)``.
:raises ValueError: If the ``interface`` is not supported.
"""
if interface == "autograd":
if optimizer == "adam":
opt = qml.AdamOptimizer(stepsize=step_size, **optimizer_kwargs)
else:
opt = qml.GradientDescentOptimizer(stepsize=step_size)
elif interface == "tf":
from .lazy_tensorflow_import import tensorflow as tf
opt = tf.keras.optimizers.SGD(learning_rate=step_size)
else:
raise ValueError('Interface "' + interface + '" is not supported.')
settings = init_settings
scores = []
samples = []
step_times = []
settings_history = [init_settings]
start_datetime = datetime.utcnow()
elapsed = 0
# performing gradient descent
for i in range(num_steps):
if i % sample_width == 0:
score = -(cost(*settings))
scores.append(score)
samples.append(i)
if verbose:
print("iteration : ", i, ", score : ", score)
start = time.time()
if interface == "autograd":
settings = opt.step(cost, *settings, grad_fn=grad_fn)
if not (isinstance(settings, list)):
settings = [settings]
elif interface == "tf":
# opt.minimize updates settings in place
tf_cost = lambda: cost(*settings)
opt.minimize(tf_cost, settings)
elapsed = time.time() - start
if i % sample_width == 0:
step_times.append(elapsed)
if verbose:
print("elapsed time : ", elapsed)
settings_history.append(settings)
opt_score = -(cost(*settings))
step_times.append(elapsed)
scores.append(opt_score)
samples.append(num_steps)
return {
"datetime": start_datetime.strftime("%Y-%m-%dT%H:%M:%SZ"),
"opt_score": opt_score,
"opt_settings": settings,
"scores": scores,
"samples": samples,
"settings_history": settings_history,
"step_times": step_times,
"step_size": step_size,
}