Gradient Descent Example Python

implementation.py

# Given f(x) = x**4 - 3**3 + 2 = f1(x) = 4x**3 - 9**2
# lets start at x = 6
curr_x = 6
gamma = 0.001
precision = 0.0000001
step_size = 1
max_iterations = 1000
i = 0

df = lambda x: (4 * x**3) - (9**2)

while step_size > precision and i < max_iterations:
  prev_x = curr_x
  curr_x -= gamma * df(prev_x)
  step_size = abs(curr_x - prev_x)
  i+=1
  
print("The local minimum occurs at:", curr_x)

pseudocode.txt

current         // Initial guess at where the optimum lies 
gamma           // A step size determined by the user 
precision       // How precise the answer must be 
step_size = 1   // The difference between the current and previous steps 
max_iterations  // How long are we willing to let the algorithm run
i = 0           // iteration counter 

def df          // Function that returns our derivative / partial derivatives

while step_size > precision and i < max_iterations:
  previous = current                  // retain the old position for comparison 
  current = gamma * - df(previous)    // the next step should be in the negative direction 
  step_size = abs(current - previous) // determine how far we have moved
  i++