Answers.Body: <p>This is standard backpropagation. The gradient term you see is in fact a <em>vector</em> of partial derivatives where each element is the partial derivative of the log-likelihood with respect to each element of the parameter vector <span class="math-container">$\theta$</span>. Therefore, it has the same dimensionality as <span class="math-container">$\theta$</span>. Each element of the parameter vector is then updated with the respective term in the vector of partial derivatives, which are generally <em>not</em> the same.</p>
  
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Answers.CreationDate: 2018-07-07T02:07:10.850Z
Answers.LastActivityDate: 2020-04-01T13:02:41.313Z
Answers.LastEditDate: 2020-04-01T13:02:41.313Z
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Body: <p>Here's the general algorithm of maximum entropy inverse reinforcement learning. </p>
  
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  <p>This uses a gradient descent algorithm. The point that I do not understand is there is only a single gradient value <span class="math-container">$\nabla_\theta \mathcal{L}$</span>, 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 <span class="math-container">$\nabla_\theta \mathcal{L}$</span>. Can you explain the logic behind updating a vector with a single gradient?</p>
  
Tags: <machine-learning><reinforcement-learning><gradient-descent><notation>
Title: What does the notation $\nabla_\theta \mathcal{L}$ mean?
UserDisplayName: İbrahim Abbasov
ThreadText: # What does the notation $\nabla_\theta \mathcal{L}$ mean?
  
  (Asked by: username_0 on 2018-07-06)
  
  Here's the general algorithm of maximum entropy inverse reinforcement learning.
  
  [![enter image description here](https://i.sstatic.net/WuBtn.jpg)](https://i.sstatic.net/WuBtn.jpg)
  
  This uses a gradient descent algorithm. The point that I do not understand is there is only a single gradient value $\nabla\_\theta \mathcal{L}$, 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 $\nabla\_\theta \mathcal{L}$. Can you explain the logic behind updating a vector with a single gradient?
  
  **Tags:** machine-learning, reinforcement-learning, gradient-descent, notation
  
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  ## 1 answers
  
  ### Answer by username_1 on 2018-07-07. Score: 4
  
  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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