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In the following, I put the link for the general algorithm of maximum entropy inverse reinforcement learning. http://178.79.149.207/assets/maxent/maxent_slide.jpg

This uses a gradient descent algorithm. The point that I do not understand is there is only a single gradient value and it is used to update a vector of parameters. To me, it does not make sense because it is updating all elements of a vector with the same value. Can you explain the logic behind updating a vector with a single gradient?

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This is standard backpropagation. The gradient term you see is in fact a vector of partial derivatives where each element is the partial derivative of the log-likelihood with respect to each element of the parameter vector \theta. Therefore, it has the same dimensionality as \theta. Each element of the parameter vector is then updated with the respective term in the vector of partial derivatives, which are generally not the same.

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