RMSprop
RMSprop, short for Root Mean Square Propagation, is an adaptive learning rate optimization algorithm designed to address some of the issues faced by traditional gradient descent methods like Gradient Descent. Here are detailed insights into RMSprop:
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Development: RMSprop was proposed by Geoff Hinton in his course on Neural Networks at the University of Toronto. It was introduced as a response to the problems with the learning rates in adaptive algorithms like AdaGrad, which can lead to very small updates late in training due to the accumulation of squared gradients.
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Functionality: RMSprop modifies the learning rate by using a moving average of squared gradients to normalize the gradient. This helps in:
- Providing a more stable and adaptive learning rate for each parameter.
- Reducing the aggressive, monotonically decreasing learning rate seen in AdaGrad.
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Algorithm: The algorithm can be described as follows:
- Initialize the moving average of squared gradients to zero.
- For each parameter update:
- Compute the gradient of the loss with respect to the parameter.
- Update the moving average of squared gradients:
E[g^2]_t = \rho * E[g^2]_{t-1} + (1 - \rho) * g_t^2, where
\rho is the decay rate, typically set between 0.9 and 0.99.
- Update the parameter:
\theta_{t+1} = \theta_t - \frac{\eta}{\sqrt{E[g^2]_t + \epsilon}} * g_t, where
\eta is the learning rate, and \epsilon is a small number to prevent division by zero.
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Advantages:
- It adapts the learning rate for each parameter, making it suitable for online and non-stationary settings where data is constantly changing.
- It helps in escaping saddle points by allowing for larger steps when gradients are small.
- Unlike AdaGrad, it does not monotonically decrease the learning rate, which helps in continuing learning even after many iterations.
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Limitations:
- Choosing the right decay rate
\rho can be challenging and might require tuning.
- RMSprop can still suffer from problems like divergence if the learning rate is too high.
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Impact: RMSprop has been influential in the development of other optimization algorithms like Adam, which combines RMSprop with momentum.
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