Optimized Gradient Descent

Putting some turbo boost into our gradient descent code

  • Bijon Setyawan Raya

  • July 18, 2022

    7 mins

    Putting some turbo boost into our gradient descent code

    Optimized Gradient Descent (2 Parts)

    In this series, we will be discussing what's wrong with my gradient descent code and how to optimize it. I wanted to make this post because whenever I did experiments with it, I should wait at least 3-5 mins to finish.

    Note that most of the code in this post is from my previous post, Gradient Descent series.

    How to Optimize?#

    Reading many blogs about Python optimization, most of the writers suggested that it was adviseable to use built-in functions and frameworks. Let's see if it's true.

    Before starting, create a new Python notebook since %%timeit only works in Python notebooks.

    If you just started learning Python, it's recommended to type the code in this post manually instead of copy and paste. Make sure that you type the code in each code block in this post into seperate code cells in your Python notebook.

    First, let's import the dataset from Scikit-learn

    from sklearn import datasets
    from timeit import timeit
    iris = datasets.load_iris()
    target =

    Once the dataset is imported, create a function so that we can test it using a Python built-in function called timeit.

    def list_append(target):
        species_names = list()
        for i in range(len(target)):
            if target[i] == 0:
            elif target[i] == 1:
        return species_names
    # Returns:
    # 61.8 µs ± 1.12 µs per loop 
    # (mean ± std. dev. of 7 runs, 10000 loops each)

    There you go! the speed turns out to be 61.8 microseconds, and that is the baseline in this entire post.

    I personally prefer typical if-else paradigm of coding since it makes the code more readable and easy to understand. Even though it makes the code look shorter, but it's rather hard for little or no relevant background programmers to understand.

    Regardless of my opinion, we are going to prove if it's faster than the baseline.

    def list_comprehension(target):
        return [
            'setosa' if i == 0 else
            'versicolor' if i == 1 else
            'virginica' for i in target
    # Returns:
    # 40.2 µs ± 274 ns per loop 
    # (mean ± std. dev. of 7 runs, 10000 loops each)

    Since using Numpy is quite common in Deep and Machine Learning projects, let's see Numpy is any better.

    def numpy_array(target):
        species_names = np.array([])
        for i in target:
            if i == 0:
                species_names = np.append(species_names, "setosa")
            elif i == 1:
                species_names = np.append(species_names, "versicolor")
                species_names = np.append(species_names, "virginica")
        return species_names
    # Returns:
    # 843 µs ± 15.2 µs per loop 
    # (mean ± std. dev. of 7 runs, 10000 loops each)

    Turned out that Numpy is way slower compared to the two previous methods. Why is it slower at appending compared to list? If you print out np.append.__doc__, you will see the following docstring.

    append : ndarray
        A copy of `arr` with `values` appended to `axis`.  Note that
        `append` does not occur in-place: a new array is allocated and
        filled.  If `axis` is None, `out` is a flattened array.

    The reason why appending elements into Numpy array is slow because it always make a copy of a thing and store it at a new array. That particular process is resource expensive.

    However, there is a work around. We can do list comprehension first and save the result in Numpy array to make it faster.

    def numpy_list_comprehension(target):
        return np.array([
            'setosa' if i == 0 else
            'versicolor' if i == 1 else
            'virginica' for i in target
    # Returns:
    # 59.6 µs ± 3.02 µs per loop 
    # (mean ± std. dev. of 7 runs, 10000 loops each)

    1. We have tested how long it takes to append elements to a list and a Numpy array
    2. There are two ways of appending elements to a list: with if-else and list comprehension
    3. Appending elements to a Numpy array is the slowest since it always make a copy of an element and store it in a new array
    4. List comprehension is the fastest method

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