Hard

RMSprop Update

~20 mincode completion

Implement rmsprop_update(weights, grad_sq, gradient, learning_rate, beta, epsilon). Return (weights_new, grad_sq_new).

Examples

Weights after update, cold start beta=0 (accessor [0])

Input
rmsprop_update([1], [0], [2], 0.1, 0, 0)
[0] of result
[0.9]

Weights: warm grad_sq normalizes step (accessor [0])

Input
rmsprop_update([0], [9], [3], 0.1, 0, 0)
[0] of result
[-0.1]

grad_sq_new accumulates (accessor [1])

Input
rmsprop_update([0], [0], [4], 0.1, 0.9, 0)
[1] of result
[1.6]

Hints

Hint 1

Take the square root at the end, not inside the sum.

Hint 2

Do not forget to 1 minus beta factor. That step is easy to skip.

Requirements

  • weights: Current weight vector

  • grad_sq: Running squared-gradient average (same shape)

  • : Current gradient

  • learning_rate: Global step size (alpha)

  • beta: Decay rate for squared gradient accumulator

  • epsilon: Numerical stability constant

  • Return Tuple (weights_new, grad_sq_new).

Constraints

  • Allowed library: NumPy only

  • Time limit: 200 ms, Memory: 64 MB

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Where this shows up

~20 min

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Python
import numpy as np

def rmsprop_update(weights: np.ndarray, grad_sq: np.ndarray, gradient: np.ndarray,
                   learning_rate: float, beta: float, epsilon: float):
    """
    Perform one RMSprop update step.

    Args:
        weights:       Current weight vector
        grad_sq:       Running squared-gradient average (same shape)
        gradient:      Current gradient
        learning_rate: Global step size (alpha)
        beta:          Decay rate for squared gradient accumulator
        epsilon:       Numerical stability constant

    Returns:
        Tuple (weights_new, grad_sq_new).
    """
    # YOUR CODE HERE
    pass
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