Easy

Implement the Gradient Descent Update

~10 mincode completion

Implement gradient_step that applies one gradient descent update to an array of parameters.

Watch out for:

  • The sign: we subtract the gradient (going downhill)
  • Modifying the original array vs. returning a new one

Examples

Correct update with lr=0.1

Input
gradient_step([2, -1], [4, -2], 0.1)
Output
[1.6, -0.8]

Zero gradients leave params unchanged

Input
gradient_step([5, 3], [0, 0], 0.5)
Output
[5, 3]

Gradient sign error detection

Input
gradient_step([1], [1], 0.1)
Output
[0.9]

Hints

Hint 1

Work directly with the arguments params, gradients, learning_rate and return the result rather than printing it.

Hint 2

Watch for this: gradient sign error.

Requirements

  • params: Current parameter values, shape (n,)

  • gradients: Gradient of loss w.r.t. params, shape (n,)

  • learning_rate: Step size alpha > 0

  • Return Updated parameters after one gradient step, shape (n,)

Constraints

  • Allowed library: NumPy only

  • Time limit: 200 ms, Memory: 64 MB

Try similar problems(3)
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Easy
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Medium
Gradient Descent for Quadratic Loss
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Where this shows up

~10 min

3 employers weight this skill

1 big tech firm, 1 frontier lab, 1 quant fund. Top match scores 80.

Python
import numpy as np

def gradient_step(
    params: np.ndarray,
    gradients: np.ndarray,
    learning_rate: float
) -> np.ndarray:
    """
    Apply one gradient descent step.

    Args:
        params:        Current parameter values, shape (n,)
        gradients:     Gradient of loss w.r.t. params, shape (n,)
        learning_rate: Step size alpha > 0

    Returns:
        Updated parameters after one gradient step, shape (n,)
    """
    # YOUR CODE HERE
    pass
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