Answers.Body: <p>Yes, since <span class="math-container">$\tilde{\theta}$</span> is a vector, to define its distribution one needs a <a href="https://en.wikipedia.org/wiki/Covariance_matrix" rel="nofollow noreferrer">covariance matrix</a>. Here <span class="math-container">$I$</span> is the identity matrix, which means that the noise has a zero-mean normal distribution with standard deviation <span class="math-container">$\sigma$</span>, and different components of this noise are uncorrelated.</p>
  
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Answers.CreationDate: 2017-10-20T21:26:22.707Z
Answers.LastActivityDate: 2019-04-01T13:53:32.710Z
Answers.LastEditDate: 2019-04-01T13:53:32.710Z
Answers.UserDisplayName: Maxim
Body: <p>In the paper <a href="https://arxiv.org/pdf/1706.01905.pdf" rel="nofollow noreferrer">Parameter Space Noise for Exploration</a>, the authors describe the noise that they add to the parameter vector as: </p>
  
  <p><span class="math-container">$$
  \tilde{\theta} = \theta + \mathcal{N}(0, \sigma^2I)
  $$</span></p>
  
  <p>is <span class="math-container">$I$</span> simply the identity matrix, or am I missing something?</p>
  
Tags: <reinforcement-learning><notation>
Title: What is $I$ in the noise described in the paper "Parameter Space Noise for Exploration"?
UserDisplayName: user6031125
ThreadText: # What is $I$ in the noise described in the paper "Parameter Space Noise for Exploration"?
  
  (Asked by: username_0 on 2017-10-19)
  
  In the paper [Parameter Space Noise for Exploration](https://arxiv.org/pdf/1706.01905.pdf), the authors describe the noise that they add to the parameter vector as:
  
  $$
  \tilde{\theta} = \theta + \mathcal{N}(0, \sigma^2I)
  $$
  
  is $I$ simply the identity matrix, or am I missing something?
  
  **Tags:** reinforcement-learning, notation
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2017-10-20. Score: 1 | Accepted answer
  
  Yes, since $\tilde{\theta}$ is a vector, to define its distribution one needs a [covariance matrix](https://en.wikipedia.org/wiki/Covariance_matrix). Here $I$ is the identity matrix, which means that the noise has a zero-mean normal distribution with standard deviation $\sigma$, and different components of this noise are uncorrelated.
  
  
  ---
  
  