import random

import numpy as np


# coding: utf-8
class MulLayer:
    def __init__(self):
        self.x = None
        self.y = None

    def forward(self, x, y):
        self.x = x
        self.y = y
        out = x * y

        return out

    def backward(self, dout):
        dx = dout * self.y
        dy = dout * self.x

        return dx, dy


class AddLayer:
    def __init__(self):
        pass

    def forward(self, x, y):
        out = x + y

        return out

    def backward(self, dout):
        dx = dout * 1
        dy = dout * 1

        return dx, dy


class PowerLayer:
    def __init__(self, power):
        self.x = None
        self.power = power
        pass

    def forward(self, x):
        out = x ** self.power
        self.x = x
        return out

    def backward(self, dout):
        dy = dout * self.power * self.x ** (self.power - 1)

        return dy


def get_data(count):
    x_data = []
    t_data = []
    for _ in range(count):
        x1 = random.random() * 200 - 100
        x2 = random.random()
        x_data.append([x1, x2])

        y = 5 * x1 + 6 * x2 + 10.1
        t_data.append(y)

    return np.array(x_data), np.array(t_data)


epoch = 100
train_size = 1000
test_size = 100
learning_rate = 1e-4

x_train, t_train = get_data(train_size)
x_test, t_test = get_data(test_size)

w1, w2, b = np.random.randn(3)

# momentum
momentum = 0.9
v_w1 = 0
v_w2 = 0
v_b = 0

# AdaGrad
h_w1 = 0
h_w2 = 0
h_b = 0

# RMSprop
decay_rate = 0.95

# Adam
idx = 0
beta1 = 0.9
beta2 = 0.999
w1_m = 0
w1_v = 0
w2_m = 0
w2_v = 0
b_m = 0
b_v = 0

w1_arr = []
w2_arr = []
b_arr = []
for _ in range(epoch):
    for i in range(train_size):
        x1, x2 = x_train[i]
        t = t_train[i]

        # forward
        z1 = x1 * w1
        z2 = x2 * w2
        z3 = z1 + z2
        z4 = z3 + b
        z5 = z4 - t
        z6 = z5 ** 2
        print(f'循环:{i} , loss:{z6}')

        # backward
        dw1 = 2 * x1 * z5
        dw2 = 2 * x2 * z5
        db = 2 * z5

        # 使用SGD
        w1 -= learning_rate * dw1
        w2 -= learning_rate * dw2
        b -= learning_rate * db

        # 使用Momentum
        # v_w1 = momentum * v_w1 - learning_rate * dw1
        # w1 += v_w1
        # v_w2 = momentum * v_w2 - learning_rate * dw2
        # w2 += v_w2
        # v_b = momentum * v_b - learning_rate * db
        # b += v_b

        # 使用AdaGrad
        # h_w1 += dw1 ** 2
        # w1 -= learning_rate * dw1 / (np.sqrt(h_w1) + 1e-7)
        # h_w2 += dw2 ** 2
        # w2 -= learning_rate * dw2 / (np.sqrt(h_w2) + 1e-7)
        # h_b += db ** 2
        # b -= learning_rate * db / (np.sqrt(h_b) + 1e-7)

        # 使用RMSprop
        # h_w1 *= decay_rate
        # h_w1 += dw1 ** 2
        # w1 -= learning_rate * dw1 / (np.sqrt(h_w1) + 1e-7)
        #
        # h_w2 *= decay_rate
        # h_w2 += dw2 ** 2
        # w2 -= learning_rate * dw2 / (np.sqrt(h_w2) + 1e-7)
        #
        # h_b *= decay_rate
        # h_b += db ** 2
        # b -= learning_rate * db / (np.sqrt(h_b) + 1e-7)

        # 使用Adam
        # idx += 1
        # lr_t = learning_rate * np.sqrt(1.0 - beta2 ** idx) / (1.0 - beta1 ** idx)
        #
        # w1_m += (1 - beta1) * (dw1 - w1_m)
        # w1_v += (1 - beta2) * (dw1 ** 2 - w1_v)
        # w1 -= lr_t * w1_m / (np.sqrt(w1_v + 1e-7))
        #
        # w2_m += (1 - beta1) * (dw2 - w2_m)
        # w2_v += (1 - beta2) * (dw2 ** 2 - w2_v)
        # w2 -= lr_t * w2_m / (np.sqrt(w2_v + 1e-7))
        #
        # b_m += (1 - beta1) * (db - b_m)
        # b_v += (1 - beta2) * (db ** 2 - b_v)
        # b -= lr_t * b_m / (np.sqrt(b_v + 1e-7))


        if i % 10 == 0:
            w1_arr.append(w1)
            w2_arr.append(w2)
            b_arr.append(b)

import matplotlib as mpl
import numpy as np
import matplotlib.pyplot as plt

mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel('w1')
ax.set_ylabel('w2')
ax.set_zlabel('b')
ax.scatter(w1_arr, w2_arr, b_arr, label='SGD')
ax.legend()

plt.show()

测试结果图片：

SGD.png

Momentum.png

rmsprop.png

AdaGrad.png

adam.png