ハイパーパラメータのチューニング手法を解説｜代表的な3つの手法を比較＆実装

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import ParameterGrid, ParameterSampler
import optuna
import pandas as pd
import logging
from mpl_toolkits.mplot3d import Axes3D
import warnings
warnings.filterwarnings("ignore")

# ========= Booth関数 =========
def booth(x, y):
    return (x + 2*y - 7)**2 + (2*x + y - 5)**2

# ========= 探索空間定義 =========
x_vals = np.linspace(-10, 10, 32)
y_vals = np.linspace(-10, 10, 32)

# 最適点 (1, 3) を確実に含める
x_vals[15] = 1.0
y_vals[23] = 3.0

param_grid = {'x': x_vals, 'y': y_vals}
all_candidates = list(ParameterGrid(param_grid))  # 32×32 = 1024点
n_trials = 1000

# ========= Grid Search =========
grid_results = [(p['x'], p['y'], booth(p['x'], p['y'])) for p in all_candidates[:n_trials]]
grid_best = min(grid_results, key=lambda x: x[2])
grid_best_index = next(i+1 for i, r in enumerate(grid_results) if r[0] == 1.0 and r[1] == 3.0)

# ========= Random Search =========
random_points = list(ParameterSampler(param_grid, n_iter=n_trials, random_state=42))
random_results = [(p['x'], p['y'], booth(p['x'], p['y'])) for p in random_points]
random_best = min(random_results, key=lambda x: x[2])
try:
    random_best_index = next(i+1 for i, r in enumerate(random_results) if r[0] == 1.0 and r[1] == 3.0)
except StopIteration:
    random_best_index = None

# ========= Bayesian Optimization =========
optuna.logging.set_verbosity(logging.WARNING) #Optuna：ログ抑制設定

def objective(trial):
    x = trial.suggest_categorical("x", list(x_vals))
    y = trial.suggest_categorical("y", list(y_vals))
    return booth(x, y)

study = optuna.create_study(direction="minimize", sampler=optuna.samplers.TPESampler(seed=42))
study.optimize(objective, n_trials=n_trials)

bayes_best = (study.best_params["x"], study.best_params["y"], study.best_value)
try:
    bayes_best_index = next(i+1 for i, t in enumerate(study.trials)
                            if t.params.get("x") == 1.0 and t.params.get("y") == 3.0)
except StopIteration:
    bayes_best_index = None

# ========= 結果表示 =========
df_results = pd.DataFrame([
    {"Method": "Grid Search", "x": grid_best[0], "y": grid_best[1],
     "f(x,y)": grid_best[2], "Step Found (x=1,y=3)": grid_best_index},
    {"Method": "Random Search", "x": random_best[0], "y": random_best[1],
     "f(x,y)": random_best[2], "Step Found (x=1,y=3)": random_best_index},
    {"Method": "Bayesian Opt", "x": bayes_best[0], "y": bayes_best[1],
     "f(x,y)": bayes_best[2], "Step Found (x=1,y=3)": bayes_best_index}
])
print("=== Booth関数 最適化結果 ===")
print(df_results)