傾斜降下法の実施

なぜ直接実施するのですか?

import numpy as np
import time

class GDOptimizer():
  history = []
  best_params = None
  best_loss = None
  
  def __init__(self, num_epochs=1000, step=0.05, learning_rate=0.1, term_threshold=0.000001, report_interval=10):
    self.num_epochs = num_epochs
    self.step = step
    self.learning_rate = learning_rate
    self.term_threshold = term_threshold
    self.report_interval = report_interval
  
  def optimize(self, my_function, params:np.array):
    t0 = time.time()
    history = []
    temp_params = None
    best_loss, best_params = np.inf, None

    for i in range(self.num_epochs):
      loss = my_function(params)
      if (len(history) > 0) and (i % self.report_interval == 0):
        print(f'{i}\t loss : {loss:.3f}, change : {abs(history[-1] - loss):.6f}, params : {params}')

      # update best loss
      if (not best_loss) or (loss < best_loss):
        best_idx = i
        best_loss = loss
        best_params = params.copy()

      # check terminate condition
      if len(history) > 0 and abs(history[-1] - loss) < self.term_threshold:
        history.append(loss)
        break
      elif self.num_epochs -1 == i:
        break
      else:
        history.append(loss)
      
      # update parameters
      temp_params = params.copy()
      for j in range(len(params)):
        temp_params[j] += self.step 
        stepped = my_function(temp_params)
        delta = stepped - loss
        params[j] -= self.learning_rate * delta
        loss = stepped
    print(f'{i}\t loss : {loss:.3f}, change : {abs(history[-1] - loss):.6f}, params : {params}')
    print(f'terminated, best idx= {best_idx}')

    result = {
        'best_loss' : best_loss,
        'best_params' : best_params,
        'history' : history,
        'time' : time.time() - t0
    }
    self.result = result
    return result

例

def my_function(params):
  # example function
  return (params[0]-3) ** 2

print('test optimizer')
print('------')
gdo = GDOptimizer(report_interval=100, term_threshold=1e-6)
result = gdo.optimize(my_function, np.ones(1))
print('------')

print('')
print(f"best loss : {result['best_loss']}")
print(f"best parmas : {result['best_params']}")

Results

test optimizer
------
100	 loss : 0.559, change : 0.010976, params : [2.25208613]
200	 loss : 0.084, change : 0.001555, params : [2.71039014]
300	 loss : 0.015, change : 0.000239, params : [2.87814423]
400	 loss : 0.004, change : 0.000043, params : [2.93954766]
500	 loss : 0.001, change : 0.000010, params : [2.9620233]
600	 loss : 0.001, change : 0.000003, params : [2.97025011]
695	 loss : 0.001, change : 0.000000, params : [2.97317178]
terminated, best idx= 695
------

best loss : 0.0007197531375624824
best parmas : [2.97317178]