Once upon a time, in the dense forests of Algorithmica, there lived a wise old Owl named Gradus. Gradus was known throughout the land for his ability to solve the most complex of puzzles using his wisdom and patience. One day, a young Rabbit named Hoppity came to Gradus with a problem. Hoppity was trying to find the best path to reach the carrot fields. He knew where he was and where he wanted to go, but the path was filled with obstacles and dangers.
Gradus listened intently and then spoke, “My dear Hoppity, to reach your destination, you must learn the way of the Gradient Descent. It is a method we wise creatures use to find the best path in the most efficient manner.”
Intrigued, Hoppity asked how it worked. Gradus explained,
“Imagine you are on top of a hill and your goal is to get to the lowest point of the valley below, where the juiciest carrots grow. The hill is covered in fog, so you can’t see the path ahead clearly. Gradient Descent is like feeling the ground beneath your feet to determine which way is downhill.”
Hoppity nodded, but he looked confused. Gradus continued,
“You take small steps in the direction that seems steepest. Each step takes you closer to your goal. However, you must be cautious. Take too large a step, and you might overshoot your destination or even end up in a worse place.”
Seeing Hoppity’s interest, Gradus took a small pebble and threw it down the hill. “Watch the pebble as it rolls down. It takes the path of least resistance, adjusting its course as it encounters different slopes. That’s how you adjust your path using the feedback you get from your surroundings.”
“But how do I know I’ve reached the best spot?” Hoppity asked, looking puzzled.
Gradus smiled and said,
“You’ll know you’re there when every step you try to take no longer leads you downhill. At that point, you’ve found the most efficient path to the juiciest carrots. That is the essence of Gradient Descent. It’s about making small, informed steps towards your goal based on the feedback you receive from your environment. And remember, patience and persistence are key. Sometimes, the path might seem longer, but it ensures that you don’t fall into hidden traps.”
Hoppity thanked Gradus for his wisdom and set out on his journey, feeling the ground beneath his feet, making small but sure steps towards the carrot fields. Along the way, he encountered many challenges but remembered Gradus’s advice. He adjusted his path based on what felt right under his feet, always moving downhill.
After some time, Hoppity reached the most bountiful carrot field he had ever seen. He realized that by applying the principle of Gradient Descent, not only had he found the best path but he had also learned a valuable lesson on problem-solving.
And so, Hoppity returned to Gradus to thank him, sharing the carrots he had gathered. Gradus nodded wisely, “Remember, Hoppity, whether in finding paths or solving problems in life, the method of Gradient Descent can guide you to your goals, step by step, by making the best use of the knowledge you gain along the way.”
And from that day on, Hoppity became known as one of the wisest creatures in Algorithmica, always ready to tackle challenges with patience, wisdom, and the principles of Gradient Descent.
What is Gradient Descent in Machine Learning?
Gradient descent in machine learning is an optimization algorithm used for finding the values of parameters (coefficients) of a function (f) that minimizes a cost function (cost). Here’s how it corresponds to the steps in the fable:
Start with a guess: Just as Hoppity knew his starting point but not the path to the carrot field, in machine learning, we start with initial guesses for the values of our model’s parameters.
Calculate the cost: This is akin to Hoppity evaluating different paths in the foggy forest to find out which way leads to the carrots. In machine learning, we calculate the cost, or how wrong our model’s predictions are, given the current parameters.
Compute the gradient: Gradus, the owl, advises Hoppity to feel the ground beneath his feet to find the downhill path. Similarly, we compute the gradient of the cost function, which tells us in which direction the cost (error) is reducing the fastest.
Make a move: Hoppity takes small, careful steps downhill, akin to how the model updates its parameters in the direction that minimizes the cost function. The size of Hoppity’s steps represents the learning rate.
Iterate: Just as Hoppity repeatedly assesses his direction and takes steps accordingly, the gradient descent algorithm iteratively adjusts the parameters, refining the model’s predictions with each step.
Convergence: When Hoppity can no longer find a downhill path, he’s reached the valley. In gradient descent, when further adjustments to the parameters no longer significantly decrease the cost, the algorithm has converged, indicating the parameters are at or near the minimum of the cost function.
Throughout Hoppity’s journey, Gradus’s wisdom mirrors the feedback loop in gradient descent, where each iteration brings us closer to our goal: the lowest point of the cost function, where the predictions of the model are the most accurate.
