"""
Implements simple stochastic gradient optimisation.
It is inspired from `_stochastic_optimizers.py
<https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/
neural_network/_stochastic_optimizers.py>`_.
"""
import numpy
from numpy.core._exceptions import UFuncTypeError
[docs]class BaseOptimizer:
"""
Base stochastic gradient descent optimizer.
:param coef: array, initial coefficient
:param learning_rate_init: float
The initial learning rate used. It controls the step-size
in updating the weights.
:param min_threshold: coefficients must be higher than *min_thresold*
:param max_threshold: coefficients must be below than *max_thresold*
The class holds the following attributes:
* *learning_rate*: float, the current learning rate
"""
def __init__(self, coef, learning_rate_init=0.1,
min_threshold=None, max_threshold=None):
if not isinstance(coef, numpy.ndarray):
raise TypeError("coef must be an array.")
self.coef = coef
self.learning_rate_init = learning_rate_init
self.learning_rate = float(learning_rate_init)
self.min_threshold = min_threshold
self.max_threshold = max_threshold
def _get_updates(self, grad):
raise NotImplementedError("Must be overwritten.") # pragma no cover
[docs] def update_coef(self, grad):
"""
Updates coefficients with given gradient.
:param grad: array, gradient
"""
if self.coef.shape != grad.shape:
raise ValueError("coef and grad must have the same shape.")
update = self._get_updates(grad)
self.coef += update
if self.min_threshold is not None:
try:
self.coef = numpy.maximum(self.coef, self.min_threshold)
except UFuncTypeError: # pragma: no cover
raise RuntimeError(
"Unable to compute an upper bound with coef={} "
"max_threshold={}".format(self.coef, self.min_threshold))
if self.max_threshold is not None:
try:
self.coef = numpy.minimum(self.coef, self.max_threshold)
except UFuncTypeError: # pragma: no cover
raise RuntimeError(
"Unable to compute a lower bound with coef={} "
"max_threshold={}".format(self.coef, self.max_threshold))
[docs] def iteration_ends(self, time_step):
"""
Performs update to learning rate and potentially other states at the
end of an iteration.
"""
pass # pragma: no cover
[docs] def train(self, X, y, fct_loss, fct_grad, max_iter=100,
early_th=None, verbose=False):
"""
Optimizes the coefficients.
:param X: datasets (array)
:param y: expected target
:param fct_loss: loss function, signature: `f(coef, X, y) -> float`
:param fct_grad: gradient function,
signature: `g(coef, x, y, i) -> array`
:param max_iter: number maximum of iteration
:param early_th: stops the training if the error goes below
this threshold
:param verbose: display information
:return: loss
"""
if not isinstance(X, numpy.ndarray):
raise TypeError("X must be an array.")
if not isinstance(y, numpy.ndarray):
raise TypeError("y must be an array.")
if X.shape[0] != y.shape[0]:
raise ValueError("X and y must have the same number of rows.")
if any(numpy.isnan(X.ravel())):
raise ValueError("X contains nan value.")
if any(numpy.isnan(y.ravel())):
raise ValueError("y contains nan value.")
loss = fct_loss(self.coef, X, y)
losses = [loss]
if verbose:
self._display_progress(0, max_iter, loss)
n_samples = 0
for it in range(max_iter):
irows = numpy.random.choice(X.shape[0], X.shape[0])
for irow in irows:
grad = fct_grad(self.coef, X[irow, :], y[irow], irow)
if isinstance(verbose, int) and verbose >= 10:
self._display_progress( # pragma: no cover
0, max_iter, loss, grad, 'grad')
if numpy.isnan(grad).sum() > 0:
raise RuntimeError( # pragma: no cover
"The gradient has nan values.")
self.update_coef(grad)
n_samples += 1
self.iteration_ends(n_samples)
loss = fct_loss(self.coef, X, y)
if verbose:
self._display_progress(it + 1, max_iter, loss)
self.iter_ = it + 1
losses.append(loss)
if self._evaluate_early_stopping(
it, max_iter, losses, early_th, verbose=verbose):
break
return loss
def _evaluate_early_stopping(
self,
it,
max_iter,
losses,
early_th,
verbose=False):
if len(losses) < 5 or early_th is None:
return False
if numpy.isnan(losses[-5]):
if numpy.isnan(losses[-1]): # pragma: no cover
if verbose:
self._display_progress(it + 1, max_iter, losses[-1],
losses=losses[-5:])
return True
return False # pragma: no cover
if numpy.isnan(losses[-1]):
if verbose: # pragma: no cover
self._display_progress(it + 1, max_iter, losses[-1],
losses=losses[-5:])
return True # pragma: no cover
if abs(losses[-1] - losses[-5]) <= early_th:
if verbose: # pragma: no cover
self._display_progress(it + 1, max_iter, losses[-1],
losses=losses[-5:])
return True
return False
def _display_progress(self, it, max_iter, loss, losses=None):
'Displays training progress.'
if losses is None: # pragma: no cover
print(f'{it}/{max_iter}: loss: {loss:1.4g}')
else:
print( # pragma: no cover
f'{it}/{max_iter}: loss: {loss:1.4g} losses: {losses}')
[docs]class SGDOptimizer(BaseOptimizer):
"""
Stochastic gradient descent optimizer with momentum.
:param coef: array, initial coefficient
:param learning_rate_init: float
The initial learning rate used. It controls the step-size
in updating the weights,
:param lr_schedule: `{'constant', 'adaptive', 'invscaling'}`,
learning rate schedule for weight updates,
`'constant'` for a constant learning rate given by
*learning_rate_init*. `'invscaling'` gradually decreases
the learning rate *learning_rate_* at each time step *t*
using an inverse scaling exponent of *power_t*.
`learning_rate_ = learning_rate_init / pow(t, power_t)`,
`'adaptive'`, keeps the learning rate constant to
*learning_rate_init* as long as the training keeps decreasing.
Each time 2 consecutive epochs fail to decrease the training loss by
tol, or fail to increase validation score by tol if 'early_stopping'
is on, the current learning rate is divided by 5.
:param momentum: float
Value of momentum used, must be larger than or equal to 0
:param power_t: double
The exponent for inverse scaling learning rate.
:param early_th: stops if the error goes below that threshold
:param min_threshold: lower bound for parameters (can be None)
:param max_threshold: upper bound for parameters (can be None)
The class holds the following attributes:
* *learning_rate*: float, the current learning rate
* velocity*: array, velocity that are used to update params
.. exref::
:title: Stochastic Gradient Descent applied to linear regression
The following example how to optimize a simple linear regression.
.. runpython::
:showcode:
import numpy
from aftercovid.optim import SGDOptimizer
def fct_loss(c, X, y):
return numpy.linalg.norm(X @ c - y) ** 2
def fct_grad(c, x, y, i=0):
return x * (x @ c - y) * 0.1
coef = numpy.array([0.5, 0.6, -0.7])
X = numpy.random.randn(10, 3)
y = X @ coef
sgd = SGDOptimizer(numpy.random.randn(3))
sgd.train(X, y, fct_loss, fct_grad, max_iter=15, verbose=True)
print('optimized coefficients:', sgd.coef)
"""
def __init__(self, coef, learning_rate_init=0.1, lr_schedule='constant',
momentum=0.9, power_t=0.5, early_th=None,
min_threshold=None, max_threshold=None):
super().__init__(coef, learning_rate_init,
min_threshold=min_threshold,
max_threshold=max_threshold)
self.lr_schedule = lr_schedule
self.momentum = momentum
self.power_t = power_t
self.early_th = early_th
self.velocity = numpy.zeros_like(coef)
[docs] def iteration_ends(self, time_step):
"""
Performs updates to learning rate and potential other states at the
end of an iteration.
:param time_step: int
number of training samples trained on so far, used to update
learning rate for 'invscaling'
"""
if self.lr_schedule == 'invscaling':
self.learning_rate = (float(self.learning_rate_init) /
(time_step + 1) ** self.power_t)
def _get_updates(self, grad):
"""
Gets the values used to update params with given gradients.
:param grad: array, gradient
:return: updates, array, the values to add to params
"""
update = self.momentum * self.velocity - self.learning_rate * grad
self.velocity = update
return update
def _display_progress(self, it, max_iter, loss, losses=None, msg='loss'):
'Displays training progress.'
if losses is None:
print(f'{it}/{max_iter}: {msg}: {loss:1.4g} '
f'lr={self.learning_rate:1.3g}')
else:
print( # pragma: no cover
'{}/{}: {}: {:1.4g} lr={:1.3g} {}es: {}'.format(
it, max_iter, msg, loss, self.learning_rate, msg, losses))
