2024.3.4 最急降下法

Gradient Descent, Steepest Descent

勾配法として最も単純なアルゴリズム

$ x_{k+1} = x_{k} - \alpha \Delta f({x_{k}})

以下、

$ y(x)=(x-1)(x-3)

$ \frac{d y}{d x} = 2x-4

について求める。

code:gd.py

import matplotlib.pyplot as plt

# y(x) = (x-1)(x-3) = x**2 - 4*x + 3

# yd(x) = 2*x - 4

def func_yd(x):

return 2*x - 4

def calc_gd(x, alpha, loopmax):

x_hist = []

for _ in range(loopmax):

x_hist.append(x)

x = x - alpha * func_yd(x)

return x_hist

##

x_initial = 3 # 初期状態

alpha = 0.1 # 学習率

loopmax = 30 # 繰り返しの上限

###

result = calc_gd(x_initial, alpha, loopmax)

plt.grid()

plt.plot(result, lw=3)

plt.legend()

plt.show()