Easy

L2 Regularization Gradient

Easy

~10 min

code completion

Gradient of L2 Regularization

When using gradient descent, we need the gradient of the regularization term with respect to the weights:

\frac{\partial}{\partial w _{i}} (λ j \sum w_{j}^{2}) = 2 λ w_{i}

In practice, this gradient is added to the task loss gradient before the parameter update:

\nabla_{total} = \nabla_{task} + 2 λ w

This is why L2 regularization is equivalent to weight decay: the update subtracts a small fraction of the current weights at every step.

Your task:

Implement l2_gradient(weights, lambda_reg) that returns $2 λ w$ .

Example Tests

Standard gradient

Input: {"weights":[1,2,3],"lambda_reg":0.1}

Expected: [0.2,0.4,0.6]

Zero weights: zero gradient

Input: {"weights":[0,0],"lambda_reg":5}

Expected: [0,0]

lambda=0.5: 2*0.5=1 so gradient equals weights

Input: {"weights":[-1,2,-3],"lambda_reg":0.5}

Expected: [-1,2,-3]

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