RMSprop

RMSprop, an abbreviation for the term Root Mean Square Propagation, is an algorithm that is designed to adjust the learning rates dynamically for training neural network models. It helps to improve the stability and speed of the training process by adapting the learning rate based on recent gradients, making it effective for training deep neural networks.

Explanation

RMSprop modifies the learning rate for each parameter individually by taking into account the magnitudes of the recent gradients to adjust the updates. Here is how it works:

• Exponential Decay of Squared Gradients: RMSprop keeps track of the moving average of the squared gradients of the loss function with an exponential decay factor. The average is then used to normalise the gradients, preventing them from being too large or too small.
• Update Rule: For each parameter $\theta_i$, RMSprop updates the exponentially decaying average of the squared gradients $E[g^2]_t$ and then uses it to adjust the parameter.

Here is an image that illustrates the update rule:

In the above image:

• $g_t$ refers to the gradient at time $t$
• $\rho$ refers to the decay rate (which is typically around $0.9$)
• $\eta$ refers to the learning rate
• $\epsilon$ refers to a small constant (around $10^{-8}$) to prevent any division by zero errors

Example

The following example demonstrates how RMSprop can be used for stochastic gradient descent:

import numpy as np

# Example neural network parameters (weights)
theta = np.array([0.2, 0.4, 0.6])

# Learning rate (step size for updating parameters)
eta = 0.01

# Decay rate (used to compute the moving average of squared gradients)
rho = 0.9

# Small constant to prevent division by zero
epsilon = 1e-8

# Running average of squared gradients
E_g2 = np.zeros_like(theta)

# Example gradients of the loss function with respect to the parameters
gradients = np.array([-0.5, 0.3, 0.24])

# Update the running average of squared gradients
E_g2 = rho * E_g2 + (1 - rho) * gradients**2

# Update the parameters using RMSprop
theta -= eta / np.sqrt(E_g2 + epsilon) * gradients

print("Updated Parameters:", theta)

The output of the above code is as follows:

Updated Parameters: [0.23162277 0.36837724 0.56837725]

Codebyte Example

The following codebyte example demonstrates the use of RMSprop in a stochastic gradient descent scenario:

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