mlstatpy.optim.sgd

class mlstatpy.optim.sgd.BaseOptimizer(coef, learning_rate_init=0.1, min_threshold=None, max_threshold=None, l1=0.0, l2=0.0)[source][source]

Base stochastic gradient descent optimizer.

Paramètres:
  • coef – array, initial coefficient

  • learning_rate_init – float The initial learning rate used. It controls the step-size in updating the weights.

  • min_threshold – coefficients must be higher than min_thresold

  • max_threshold – coefficients must be below than max_thresold

The class holds the following attributes:

  • learning_rate: float, the current learning rate

  • coef: optimized coefficients

  • min_threshold, max_threshold: coefficients thresholds

  • l2: L2 regularization

  • l1: L1 regularization

iteration_ends(time_step)[source][source]

Performs update to learning rate and potentially other states at the end of an iteration.

train(X, y, fct_loss, fct_grad, max_iter=100, early_th=None, verbose=False)[source][source]

Optimizes the coefficients.

Paramètres:
  • X – datasets (array)

  • y – expected target

  • fct_loss – loss function, signature: f(coef, X, y) -> float

  • fct_grad – gradient function, signature: g(coef, x, y, i) -> array

  • max_iter – number maximum of iteration

  • early_th – stops the training if the error goes below this threshold

  • verbose – display information

Renvoie:

loss

The method keeps the best coefficients for the minimal loss.

update_coef(grad)[source][source]

Updates coefficients with given gradient.

Paramètres:

grad – array, gradient

class mlstatpy.optim.sgd.SGDOptimizer(coef, learning_rate_init=0.1, lr_schedule='invscaling', momentum=0.9, power_t=0.5, early_th=None, min_threshold=None, max_threshold=None, l1=0.0, l2=0.0)[source][source]

Stochastic gradient descent optimizer with momentum.

Paramètres:
  • coef – array, initial coefficient

  • learning_rate_init – float The initial learning rate used. It controls the step-size in updating the weights,

  • 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.

  • momentum – float Value of momentum used, must be larger than or equal to 0

  • power_t – double The exponent for inverse scaling learning rate.

  • early_th – stops if the error goes below that threshold

  • min_threshold – lower bound for parameters (can be None)

  • max_threshold – upper bound for parameters (can be None)

  • l1 – L1 regularization

  • l2 – L2 regularization

The class holds the following attributes:

  • learning_rate: float, the current learning rate

  • velocity*: array, velocity that are used to update params

Stochastic Gradient Descent applied to linear regression

The following example how to optimize a simple linear regression.

<<<

import numpy
from mlstatpy.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)

>>>

    0/15: loss: 49.82 lr=0.1 max(coef): 1.3 l1=0/3 l2=0/3.1
    1/15: loss: 13.98 lr=0.0302 max(coef): 0.8 l1=0.088/1.5 l2=0.0054/1.1
    2/15: loss: 3.738 lr=0.0218 max(coef): 0.63 l1=0.022/1.3 l2=0.00018/0.67
    3/15: loss: 1.999 lr=0.018 max(coef): 0.72 l1=0.24/1.4 l2=0.02/0.83
    4/15: loss: 1.567 lr=0.0156 max(coef): 0.8 l1=0.06/1.5 l2=0.0026/0.93
    5/15: loss: 1.402 lr=0.014 max(coef): 0.82 l1=0.0064/1.6 l2=1.8e-05/0.99
    6/15: loss: 1.126 lr=0.0128 max(coef): 0.81 l1=0.036/1.6 l2=0.00045/0.97
    7/15: loss: 0.925 lr=0.0119 max(coef): 0.79 l1=0.00078/1.6 l2=2.2e-07/0.95
    8/15: loss: 0.7864 lr=0.0111 max(coef): 0.77 l1=0.0012/1.6 l2=5.3e-07/0.93
    9/15: loss: 0.6454 lr=0.0105 max(coef): 0.76 l1=0.0088/1.6 l2=3.3e-05/0.91
    10/15: loss: 0.5454 lr=0.00995 max(coef): 0.74 l1=0.042/1.6 l2=0.0012/0.89
    11/15: loss: 0.4745 lr=0.00949 max(coef): 0.73 l1=0.039/1.6 l2=0.001/0.88
    12/15: loss: 0.4059 lr=0.00909 max(coef): 0.71 l1=0.11/1.6 l2=0.0041/0.86
    13/15: loss: 0.363 lr=0.00874 max(coef): 0.71 l1=0.047/1.6 l2=0.00086/0.86
    14/15: loss: 0.3138 lr=0.00842 max(coef): 0.7 l1=0.0037/1.6 l2=5.1e-06/0.85
    15/15: loss: 0.2867 lr=0.00814 max(coef): 0.69 l1=0.083/1.6 l2=0.0028/0.85
    optimized coefficients: [ 0.415  0.691 -0.45 ]
iteration_ends(time_step)[source][source]

Performs updates to learning rate and potential other states at the end of an iteration.

Paramètres:

time_step – int number of training samples trained on so far, used to update learning rate for “invscaling”