How To Calculate Gradient Descent By Hand

Gradient Descent Formula:

\[ \theta_{new} = \theta_{old} - \alpha \times \frac{\partial J}{\partial \theta} \]

New Parameter (θ_new):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Gradient Descent?

Gradient descent is an optimization algorithm used to minimize functions by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. It is widely used in machine learning and deep learning for training models.

2. How Does The Calculator Work?

The calculator uses the gradient descent formula:

\[ \theta_{new} = \theta_{old} - \alpha \times \frac{\partial J}{\partial \theta} \]

Where:

\( \theta_{new} \) — New parameter value after update
\( \theta_{old} \) — Current parameter value
\( \alpha \) — Learning rate (step size)
\( \frac{\partial J}{\partial \theta} \) — Gradient of the cost function with respect to the parameter

Explanation: The algorithm updates parameters by subtracting the product of learning rate and gradient from the current parameter value, moving towards the minimum of the cost function.

3. Importance Of Gradient Descent

Details: Gradient descent is fundamental to machine learning as it enables models to learn from data by minimizing loss functions. It is used in linear regression, neural networks, and various other machine learning algorithms.

4. Using The Calculator

Tips: Enter the current parameter value, learning rate (typically a small positive number like 0.01 or 0.001), and the computed gradient. The calculator will output the updated parameter value.

5. Frequently Asked Questions (FAQ)

Q1: What is the learning rate?
A: The learning rate determines the step size at each iteration while moving toward a minimum of the loss function. Too large can cause overshooting, too small can make convergence slow.

Q2: What are common learning rate values?
A: Typical values range from 0.001 to 0.1, but the optimal value depends on the specific problem and should be determined through experimentation.

Q3: What is the gradient?
A: The gradient is the vector of partial derivatives of the cost function with respect to each parameter. It points in the direction of steepest ascent.

Q4: What are the types of gradient descent?
A: Batch gradient descent (uses entire dataset), Stochastic gradient descent (uses one sample), and Mini-batch gradient descent (uses small batches).

Q5: When does gradient descent converge?
A: Gradient descent converges when the gradient approaches zero or when changes in the cost function become negligible between iterations.