Numpy实现优化器

Posted 2021-10-11 AI小浩

import numpy as np
from mlfromscratch.utils import make_diagonal, normalize

# Optimizers for models that use gradient based methods for finding the 
# weights that minimizes the loss.
# A great resource for understanding these methods: 
# http://sebastianruder.com/optimizing-gradient-descent/index.html

class StochasticGradientDescent():
def __init__(self, learning_rate=0.01, momentum=0):
self.learning_rate = learning_rate 
self.momentum = momentum
self.w_updt = None

def update(self, w, grad_wrt_w):
# If not initialized
if self.w_updt is None:
self.w_updt = np.zeros(np.shape(w))
# Use momentum if set
self.w_updt = self.momentum * self.w_updt + (1 - self.momentum) * grad_wrt_w
# Move against the gradient to minimize loss
return w - self.learning_rate * self.w_updt

class NesterovAcceleratedGradient():
def __init__(self, learning_rate=0.001, momentum=0.4):
self.learning_rate = learning_rate 
self.momentum = momentum
self.w_updt = np.array([])

def update(self, w, grad_func):
# Calculate the gradient of the loss a bit further down the slope from w
approx_future_grad = np.clip(grad_func(w - self.momentum * self.w_updt), -1, 1)
# Initialize on first update
if not self.w_updt.any():
self.w_updt = np.zeros(np.shape(w))

self.w_updt = self.momentum * self.w_updt + self.learning_rate * approx_future_grad
# Move against the gradient to minimize loss
return w - self.w_updt

class Adagrad():
def __init__(self, learning_rate=0.01):
self.learning_rate = learning_rate
self.G = None # Sum of squares of the gradients
self.eps = 1e-8

def update(self, w, grad_wrt_w):
# If not initialized
if self.G is None:
self.G = np.zeros(np.shape(w))
# Add the square of the gradient of the loss function at w
self.G += np.power(grad_wrt_w, 2)
# Adaptive gradient with higher learning rate for sparse data
return w - self.learning_rate * grad_wrt_w / np.sqrt(self.G + self.eps)

class Adadelta():
def __init__(self, rho=0.95, eps=1e-6):
self.E_w_updt = None # Running average of squared parameter updates
self.E_grad = None   # Running average of the squared gradient of w
self.w_updt = None   # Parameter update
self.eps = eps
self.rho = rho

def update(self, w, grad_wrt_w):
# If not initialized
if self.w_updt is None:
self.w_updt = np.zeros(np.shape(w))
self.E_w_updt = np.zeros(np.shape(w))
self.E_grad = np.zeros(np.shape(grad_wrt_w))

# Update average of gradients at w
self.E_grad = self.rho * self.E_grad + (1 - self.rho) * np.power(grad_wrt_w, 2)

RMS_delta_w = np.sqrt(self.E_w_updt + self.eps)
RMS_grad = np.sqrt(self.E_grad + self.eps)

# Adaptive learning rate
adaptive_lr = RMS_delta_w / RMS_grad

# Calculate the update
self.w_updt = adaptive_lr * grad_wrt_w

# Update the running average of w updates
self.E_w_updt = self.rho * self.E_w_updt + (1 - self.rho) * np.power(self.w_updt, 2)

return w - self.w_updt

class RMSprop():
def __init__(self, learning_rate=0.01, rho=0.9):
self.learning_rate = learning_rate
self.Eg = None # Running average of the square gradients at w
self.eps = 1e-8
self.rho = rho

def update(self, w, grad_wrt_w):
# If not initialized
if self.Eg is None:
self.Eg = np.zeros(np.shape(grad_wrt_w))

self.Eg = self.rho * self.Eg + (1 - self.rho) * np.power(grad_wrt_w, 2)

# Divide the learning rate for a weight by a running average of the magnitudes of recent
# gradients for that weight
return w - self.learning_rate *  grad_wrt_w / np.sqrt(self.Eg + self.eps)

class Adam():
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