What is gradient descent?

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Gradient Descent

• Gradient Descent is an optimization algorithm used to minimize a loss function (the error between predicted and actual values).

• It works by iteratively adjusting model parameters (weights & biases) in the direction that reduces error the fastest.

How It Works (Steps)

1. Initialize Weights → Start with random values for weights.

2. Compute Loss → Measure error using a loss function (e.g., Mean Squared Error, Cross-Entropy).

3. Calculate Gradient → Find the slope (derivative) of the loss function w.r.t each weight.

4. Update Weights → Adjust weights using the rule:

   $$w = w - \eta \cdot \frac{\partial L}{\partial w}$$

   • $w$ = weight

   • $\eta$ = learning rate (step size)

   • $\frac{\partial L}{\partial w}$ = gradient (slope of loss w.r.t weight)

5. Repeat → Continue until the loss is minimized or convergence is reached.

Types of Gradient Descent

1. Batch Gradient Descent → Uses the whole dataset for each update.

2. Stochastic Gradient Descent (SGD) → Updates weights after each training sample (faster, but noisier).

3. Mini-batch Gradient Descent → Uses a subset of data for each update (most common).

Real-World Analogy

Imagine you’re on top of a hill (high error) and want to reach the valley (minimum error).

• The slope of the hill tells you the direction to step (gradient).

• The step size you take = learning rate.

• Small steps = slow but safe, large steps = fast but may overshoot.

✅ In short:

Gradient Descent = method of finding the best weights for a model by gradually moving downhill on the error curve until the loss is minimized.

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