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Is there a theoretical way to determine the best learning rate for gradient descent if the function is a simple known polynomial?

You are considering a one-dimensional parabola; in this case, it is easy. The derivative is twice the distance to the optimal point, so the optimal learning rate is always 0.5/a, where a is coef near ...
Kirill Fedyanin's user avatar
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Papers on gradient descent w.r.t inputs for optimization

You can optimise an input $x$ to produce a minimum or maximum $y$ where $y = f(x)$ using gradient methods: Provided $f(x)$ is differentiable. If $f(x)$ is composed of multiple functions $f(x) = n \...
Neil Slater's user avatar
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Papers on gradient descent w.r.t inputs for optimization

Im assuming you are talking about changing input vector of features with gradient descent to optimise the loss function of your choice, while keeping the already trained model weights frozen. It is a ...
vl_knd's user avatar
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REINFORCE with Baseline update rule

The value $\delta$ is already representing a derivative equivalent to derivative of MSE loss for the difference between observed and predicted return. Multiplying it by the gradient of $\hat{v}$ to ...
Neil Slater's user avatar
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Papers on gradient descent w.r.t inputs for optimization

there are method that "change the inputs to have a better output"... they are called GANs (and if you are very creative, you might also see diffusion models as such)
Alberto's user avatar
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What do you mean by "updating based on a training example/batch" in Gradient Descent?

In batch gradient descent computing the loss function every time serves several purposes. While the value of the loss itself may not directly affect the backpropagation process, as you said monitoring ...
cinch's user avatar
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Can you explain the Hinton's comment "Rprop is equivalent to using the gradient, but also dividing by the size of the gradient"?

"Rprop is equivalent to using the gradient" means Rprop fundamentally relies on information about the sign of the gradient of each weight to determine the direction of weight updates. Like ...
cinch's user avatar
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