Answers.Body: <p>Normalization, also known as scaling or standardization of input features, is essential not only in Reinforcement Learning but in machine learning in general. Normalization is widely accepted as a good practice, particularly when dealing with features that vary in scale and range. By doing so, you help ensure that the training process is both stable and efficient.</p>
  <p>Here are a couple of main reasons:</p>
  <p><strong>Convergence Speed</strong>: Normalized inputs can accelerate the convergence of the algorithm by ensuring that the gradient descent steps are balanced across all dimensions. Without normalization, features with larger scales dominate the gradient updates, which can lead to slower convergence or divergence.</p>
  <p><a href="https://i.sstatic.net/7P5DQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7P5DQ.png" alt="gradient descent." /></a>
  (<a href="https://www.jeremyjordan.me/batch-normalization/" rel="nofollow noreferrer">source</a>)</p>
  <p><strong>Equal Contribution</strong>: By scaling features to a similar range, you encourage the model to consider all features equally during learning. Otherwise, features with larger magnitudes may have a disproportionate influence on the distance metrics, loss calculation, and learned weights.</p>
  <p><strong>Better Learning Rate Generalization</strong>: When features are normalized, the learning rate parameter becomes more general and less dependent on the scale of the features. It's easier to find a suitable learning rate that works well across all features.</p>
  <p><a href="https://i.sstatic.net/NamiY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NamiY.png" alt="learning rate" /></a>
  (<a href="https://www.jeremyjordan.me/batch-normalization/" rel="nofollow noreferrer">source</a>)</p>
  <p>The normalization is done not only for the input data but also for intermediate layers. Features with large values can cause numerical instability, leading to issues such as exploding gradients in neural networks. Normalization keeps the values within a controlled range, contributing to the numerical stability of the training process. You can read more on it in <a href="https://arxiv.org/abs/1502.03167" rel="nofollow noreferrer">Bach Normalization</a> and <a href="https://arxiv.org/abs/1803.08494v3" rel="nofollow noreferrer">Group Normalization</a> papers. These papers provide theoretical information on normalization in general. We can consider the output of each hidden layer as an input to the next one. So some insights are also useful to understand normalization of the input data.</p>
  <p>Depending on your data you may choose different approaches for normalizing your input data. For example, for images, it could be a simple mapping of pixel intensities [0, 255] to [0, 1] or [-1, 1] range.</p>
  <p>Another common practice is to calculate the mean and standard deviation of your training set for normalization.</p>
  <p>One more technique is min-max scaling, where each feature is scaled to a range [0, 1] or [-1, 1] by subtracting the minimum value and dividing by the range.</p>
  <p>It's important to note that you should not recompute the mean and standard deviation for normalization during the testing phase or while the model is in production. Use the statistics computed from the training set to avoid any leakage and to ensure consistency between the training and testing normalization processes.</p>
  
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Answers.CreationDate: 2024-01-09T15:59:18.040Z
Answers.Text: This is a lot of useful information about normalisation, but fails to address the question. The OP needs to understand how to approach normalisation when using an online + replay structure in a DQN. They cannot apply standard normalisation techniques because they don't have a complete training dataset at the start of training. Batch normalisation is not really in scope here either, they are asking about input features not NN architecture
Answers.UserDisplayName: Neil Slater
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Answers.CreationDate: 2024-01-09T16:06:17.717Z
Answers.Text: @NeilSlater Since we are speaking about DQN (which is a neural network), the normalization directly addresses the question. Without further information about the source of the data, there is nothing to add. Regarding BN and GN, these papers provide theoretical information on normalization in general. We can consider the output of each hidden layer as an input. So this also applies to the normalization of the input data
Answers.UserDisplayName: Aray Karjauv
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Answers.CreationDate: 2024-01-12T02:28:34.967Z
Answers.Text: Thanks for the detailed explanation @ArayKarjauv. But I don't understand how to apply this in the context of online + replay structure in a DQN. How do I calculate the mean and standard deviation to do this when I don't have a full dataset and if I am to use a running average how do I do this?
Answers.UserDisplayName: Aki A
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Answers.Text: @AkiA can you provide us with more details on your data? otherwise, if you know the range of your data, you can always standardize it by mapping it to a smaller range
Answers.UserDisplayName: Aray Karjauv
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Answers.CreationDate: 2024-01-09T15:54:27.180Z
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Answers.LastEditDate: 2024-01-09T16:20:33.487Z
Answers.UserDisplayName: Aray Karjauv
Body: <p>There are 4 features in my state representation and they are in different ranges. So I'm thinking state normalization would reduce the bias on certain features. And also, in the problem I consider, there is a distribution shift in the inputs between train and test times. I think state normalization would help both issues.I found some suggestions in this question <a href="https://ai.stackexchange.com/questions/41229/how-would-one-normalize-observations-in-off-policy-online-reinforcement-learning">here</a></p>
  <p>Can someone provide an example where this is done? It's a bit confusing to me.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-01-07T20:59:26.690Z
Comments.Text: Can you explain what you know about "state space normalization"? Also, why are you interested in this? Thanks for providing more context.
Comments.UserDisplayName: nbro
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Comments.Text: there are 4 features in my state representation and they are in different ranges. So I'm thinking state normalization would reduce the bias on certain features. And also, in the problem I consider, there is a distribution shift in the inputs between train and test times. I think state normalization would help both issues.
Comments.UserDisplayName: Aki A
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Comments.CreationDate: 2024-01-08T00:06:23.917Z
Comments.Text: Thanks for clarifying this. Can you please include this info in your post.
Comments.UserDisplayName: nbro
Tags: <reinforcement-learning><deep-rl><dqn>
Title: How is state space normalization done in off-policy algorithms like dqn?
UserDisplayName: Aki A
ThreadText: # How is state space normalization done in off-policy algorithms like dqn?
  
  (Asked by: username_0 on 2024-01-07)
  
  There are 4 features in my state representation and they are in different ranges. So I'm thinking state normalization would reduce the bias on certain features. And also, in the problem I consider, there is a distribution shift in the inputs between train and test times. I think state normalization would help both issues.I found some suggestions in this question [here](https://ai.stackexchange.com/questions/41229/how-would-one-normalize-observations-in-off-policy-online-reinforcement-learning)
  
  Can someone provide an example where this is done? It's a bit confusing to me.
  
  **Tags:** reinforcement-learning, deep-rl, dqn
  
  > **Comments:**
  > **username_1**: Can you explain what you know about "state space normalization"? Also, why are you interested in this? Thanks for providing more context.  
  > **username_0**: there are 4 features in my state representation and they are in different ranges. So I'm thinking state normalization would reduce the bias on certain features. And also, in the problem I consider, there is a distribution shift in the inputs between train and test times. I think state normalization would help both issues.  
  > **username_1**: Thanks for clarifying this. Can you please include this info in your post.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2024-01-09. Score: 0
  
  Normalization, also known as scaling or standardization of input features, is essential not only in Reinforcement Learning but in machine learning in general. Normalization is widely accepted as a good practice, particularly when dealing with features that vary in scale and range. By doing so, you help ensure that the training process is both stable and efficient.
  
  Here are a couple of main reasons:
  
  **Convergence Speed**: Normalized inputs can accelerate the convergence of the algorithm by ensuring that the gradient descent steps are balanced across all dimensions. Without normalization, features with larger scales dominate the gradient updates, which can lead to slower convergence or divergence.
  
  [![gradient descent.](https://i.sstatic.net/7P5DQ.png)](https://i.sstatic.net/7P5DQ.png)
  ([source](https://www.jeremyjordan.me/batch-normalization/))
  
  **Equal Contribution**: By scaling features to a similar range, you encourage the model to consider all features equally during learning. Otherwise, features with larger magnitudes may have a disproportionate influence on the distance metrics, loss calculation, and learned weights.
  
  **Better Learning Rate Generalization**: When features are normalized, the learning rate parameter becomes more general and less dependent on the scale of the features. It's easier to find a suitable learning rate that works well across all features.
  
  [![learning rate](https://i.sstatic.net/NamiY.png)](https://i.sstatic.net/NamiY.png)
  ([source](https://www.jeremyjordan.me/batch-normalization/))
  
  The normalization is done not only for the input data but also for intermediate layers. Features with large values can cause numerical instability, leading to issues such as exploding gradients in neural networks. Normalization keeps the values within a controlled range, contributing to the numerical stability of the training process. You can read more on it in [Bach Normalization](https://arxiv.org/abs/1502.03167) and [Group Normalization](https://arxiv.org/abs/1803.08494v3) papers. These papers provide theoretical information on normalization in general. We can consider the output of each hidden layer as an input to the next one. So some insights are also useful to understand normalization of the input data.
  
  Depending on your data you may choose different approaches for normalizing your input data. For example, for images, it could be a simple mapping of pixel intensities [0, 255] to [0, 1] or [-1, 1] range.
  
  Another common practice is to calculate the mean and standard deviation of your training set for normalization.
  
  One more technique is min-max scaling, where each feature is scaled to a range [0, 1] or [-1, 1] by subtracting the minimum value and dividing by the range.
  
  It's important to note that you should not recompute the mean and standard deviation for normalization during the testing phase or while the model is in production. Use the statistics computed from the training set to avoid any leakage and to ensure consistency between the training and testing normalization processes.
  
  > **Comments:**
  > **username_3**: This is a lot of useful information about normalisation, but fails to address the question. The OP needs to understand how to approach normalisation when using an online + replay structure in a DQN. They cannot apply standard normalisation techniques because they don't have a complete training dataset at the start of training. Batch normalisation is not really in scope here either, they are asking about input features not NN architecture  
  > **username_2**: @username_3 Since we are speaking about DQN (which is a neural network), the normalization directly addresses the question. Without further information about the source of the data, there is nothing to add. Regarding BN and GN, these papers provide theoretical information on normalization in general. We can consider the output of each hidden layer as an input. So this also applies to the normalization of the input data  
  > **username_0**: Thanks for the detailed explanation @username_2. But I don't understand how to apply this in the context of online + replay structure in a DQN. How do I calculate the mean and standard deviation to do this when I don't have a full dataset and if I am to use a running average how do I do this?  
  > **username_2**: @username_0 can you provide us with more details on your data? otherwise, if you know the range of your data, you can always standardize it by mapping it to a smaller range  
  
  ---
  
  