2024.7.10 optimを用いた勾配法による最適化【torch】

code:optim1.py

import torch as pt

import matplotlib.pyplot as plt

import torch.optim as optim

def func(x):

return x**2 -2*x - 3

# >>> パラメータ

x0 = 2.0 # 初期値をint型で用意

alpha = 0.1 # 学習率

hist_x = []

# <<<

x = pt.tensor(x0, dtype=pt.float, requires_grad=True)

for i in range(50):

hist_x.append(x.detach().clone())

optimizer.zero_grad()

y = func(x)

y.backward() # x.grad を求める

optimizer.step() # x.grad を用いて x を更新

hist_x.append(x.detach().clone()) # 最後の１つをアペンド

hist_x = pt.stack(hist_x)

plt.plot(hist_x)

plt.show()

可視化してみる。

code:optim2.py

import torch as pt

import numpy as np

import matplotlib.pyplot as plt

import torch.optim as optim

def func(x):

return x**2 -2*x - 3

# >>> パラメータ

x0 = 2.0

alpha = 0.1

hist_x = []

hist_y = []

# <<<

x = pt.tensor(x0, dtype=pt.float, requires_grad=True)

y = func(x)

for i in range(50):

hist_x.append(x.detach().numpy().copy())

optimizer.zero_grad()

y = func(x)

y.backward()

optimizer.step()

hist_y.append(y.detach().clone())

hist_x = np.stack(hist_x)

hist_y = np.stack(hist_y)

x = np.linspace(0.5, 2)

y = func(x)

plt.plot(x, y)

plt.plot(hist_x, hist_y, '*')

plt.grid()

plt.show()

https://scrapbox.io/files/668ddba3c18aa5001cde94ee.png

４次関数の例

code:opt3.py

import torch as pt

import numpy as np

import matplotlib.pyplot as plt

import torch.optim as optim

def func(x):

return (2*x + 1)*(x + 2)*(x - 1)*x

# >>> パラメータ

x0 = 0.0

alpha = 0.01

hist_x = []

hist_y = []

# <<<

x = pt.tensor(x0, dtype=pt.float, requires_grad=True)

y = func(x)

for i in range(50):

hist_x.append(x.detach().numpy().copy())

optimizer.zero_grad()

y = func(x)

y.backward()

optimizer.step()

hist_y.append(y.detach().numpy().copy())

hist_x = np.stack(hist_x)

hist_y = np.stack(hist_y)

x = np.linspace(-2.1, 1.1) # デフォルトでは50点

y = func(x)

plt.plot(x, y)

plt.plot(hist_x, hist_y, '*')

plt.grid()

plt.show()

結果は初期値に依存することがよくわかる。

https://scrapbox.io/files/668dddb3859fb3001cb76f9b.png