神经网络最优化方法比较(代码理解)

时间:2024-03-16 15:01:57

为高效找到使损失函数的值最小的参数,关于最优化(optimization)提了很多方法。

http://ruder.io/optimizing-gradient-descent/  本网页介绍的原理可以参考。下面这段代码取自一本教材,比较经典。

# coding: utf-8
import numpy as np
import matplotlib.pyplot as plt
from collections import OrderedDict

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] += (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)

            
def f(x, y):
    return x**2 / 20.0 + y**2


def df(x, y):
    return x / 10.0, 2.0*y

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

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'])
        optimizer.update(params, grads)
    

    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)#绘制等高线
    plt.ylim(-10, 10)
    plt.xlim(-10, 10)
    plt.plot(0, 0, '+')
    plt.title(key)
    plt.xlabel("x")
    plt.ylabel("y")
    
plt.subplots_adjust(wspace =0, hspace =0)#调整子图间距
plt.show()

 神经网络最优化方法比较(代码理解)