# coding: utf-8
import sys, os
sys.path.append(os.pardir) # 为了导入父目录的文件而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from collections import OrderedDict
from common.optimizer import *
#原函数
def f(x, y):
return x**2 / 20.0 + y**2
#函数求导
def df(x, y):
return x / 10.0, 2.0*y
#选择一个点
init_pos = (-7.0, 2.0)
params = {}
params['x'], params['y'] = init_pos[0], init_pos[1]
grads = {}
grads['x'], grads['y'] = 0, 0
optimizers = OrderedDict()
optimizers["SGD"] = SGD(lr=0.95)
optimizers["Momentum"] = Momentum(lr=0.1)
optimizers["AdaGrad"] = AdaGrad(lr=1.5)
optimizers["Adam"] = Adam(lr=0.3)
idx = 1
#遍历每种方法
for key in optimizers:
optimizer = optimizers[key]
x_history = []
y_history = []
params['x'], params['y'] = init_pos[0], init_pos[1]
for i in range(30):
x_history.append(params['x'])
y_history.append(params['y'])
grads['x'], grads['y'] = df(params['x'], params['y'])
#更新参数
optimizer.update(params, grads)
#画图
x = np.arange(-10, 10, 0.01)
y = np.arange(-5, 5, 0.01)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)
# for simple contour line
mask = Z > 7
Z[mask] = 0
# plot
plt.subplot(2, 2, idx)
idx += 1
plt.plot(x_history, y_history, 'o-', color="red")
plt.contour(X, Y, Z)
plt.ylim(-10, 10)
plt.xlim(-10, 10)
plt.plot(0, 0, '+')
#colorbar()
#spring()
plt.title(key)
plt.xlabel("x")
plt.ylabel("y")
plt.show()
核心算法实现
# coding: utf-8
import numpy as np
class SGD:
"""随机梯度下降法（Stochastic Gradient Descent）"""
def __init__(self, lr=0.01):
self.lr = lr
def update(self, params, grads):
for key in params.keys():
params[key] -= self.lr * grads[key]
class Momentum:
"""Momentum SGD"""
def __init__(self, lr=0.01, momentum=0.9):
self.lr = lr
self.momentum = momentum
self.v = None
def update(self, params, grads):
if self.v is None:
self.v = {}
for key, val in params.items():
self.v[key] = np.zeros_like(val)
for key in params.keys():
self.v[key] = self.momentum*self.v[key] - self.lr*grads[key]
params[key] += self.v[key]
class Nesterov:
"""Nesterov's Accelerated Gradient (http://arxiv.org/abs/1212.0901)"""
def __init__(self, lr=0.01, momentum=0.9):
self.lr = lr
self.momentum = momentum
self.v = None
def update(self, params, grads):
if self.v is None:
self.v = {}
for key, val in params.items():
self.v[key] = np.zeros_like(val)
for key in params.keys():
self.v[key] *= self.momentum
self.v[key] -= self.lr * grads[key]
params[key] += self.momentum * self.momentum * self.v[key]
params[key] -= (1 + self.momentum) * self.lr * grads[key]
class AdaGrad:
"""AdaGrad"""
def __init__(self, lr=0.01):
self.lr = lr
self.h = None
def update(self, params, grads):
if self.h is None:
self.h = {}
for key, val in params.items():
self.h[key] = np.zeros_like(val)
for key in params.keys():
self.h[key] += grads[key] * grads[key]
params[key] -= self.lr * grads[key] / (np.sqrt(self.h[key]) + 1e-7)
class RMSprop:
"""RMSprop"""
def __init__(self, lr=0.01, decay_rate = 0.99):
self.lr = lr
self.decay_rate = decay_rate
self.h = None
def update(self, params, grads):
if self.h is None:
self.h = {}
for key, val in params.items():
self.h[key] = np.zeros_like(val)
for key in params.keys():
self.h[key] *= self.decay_rate
self.h[key] += (1 - self.decay_rate) * grads[key] * grads[key]
params[key] -= self.lr * grads[key] / (np.sqrt(self.h[key]) + 1e-7)
class Adam:
"""Adam (http://arxiv.org/abs/1412.6980v8)"""
def __init__(self, lr=0.001, beta1=0.9, beta2=0.999):
self.lr = lr
self.beta1 = beta1
self.beta2 = beta2
self.iter = 0
self.m = None
self.v = None
def update(self, params, grads):
if self.m is None:
self.m, self.v = {}, {}
for key, val in params.items():
self.m[key] = np.zeros_like(val)
self.v[key] = np.zeros_like(val)
self.iter += 1
lr_t = self.lr * np.sqrt(1.0 - self.beta2**self.iter) / (1.0 - self.beta1**self.iter)
for key in params.keys():
#self.m[key] = self.beta1*self.m[key] + (1-self.beta1)*grads[key]
#self.v[key] = self.beta2*self.v[key] + (1-self.beta2)*(grads[key]**2)
self.m[key] += (1 - self.beta1) * (grads[key] - self.m[key])
self.v[key] += (1 - self.beta2) * (grads[key]**2 - self.v[key])
params[key] -= lr_t * self.m[key] / (np.sqrt(self.v[key]) + 1e-7)
#unbias_m += (1 - self.beta1) * (grads[key] - self.m[key]) # correct bias
#unbisa_b += (1 - self.beta2) * (grads[key]*grads[key] - self.v[key]) # correct bias
#params[key] += self.lr * unbias_m / (np.sqrt(unbisa_b) + 1e-7)