Answers.Body: <blockquote>
  <p>One way to handle this, is to keep the target policy close to the
  behavior policy by regularizing, for example by using a KL divergence
  penalty. So when the target policy deviates too much from the behavior
  one, it gets a penalty for the learning objective.</p>
  </blockquote>
  <p>Regularizing the target policy to be close to the behavior policy has been done with some success in previous works (e.g. see Related Work section of the Conservative Q-Learning <a href="https://arxiv.org/abs/2006.04779" rel="nofollow noreferrer">paper</a>). The regularizer acts as a safeguard by preventing unrealistically high queried values of unseen state-action pairs to heavily influence the expected values of the target policy in the bootstrapping update. Since you have seen this method used before, I will not expand further.</p>
  <blockquote>
  <p>Another way, if I understood the concept of IS correctly, would be to
  introduce importance sampling to estimate the expected values from
  samples that are drawn from the  behavior policy w.r.t to the target
  policy. This would keep the  distribution close to the target
  policy...</p>
  </blockquote>
  <p>You are correct in that importance sampling will estimate the expected values of the target policy from samples drawn from the behavior policy. However, importance sampling does not act as a safeguard as described previously. Specifically, implementing a reweighting scheme such as importance sampling when calculating the expected values does not prevent the agent from querying unseen state-action pairs. If these queried values are unrealistically high, then the target policy will learn to take those actions more often. This will result in an increase of the importance sampling weights corresponding to those state-action pairs, which will ultimately result in unrealistically high expected values of the target policy. From another point of view, the importance sampling weights for the state-action pairs with unrealistically high queried values may start small, but there is no safeguard against the weights increasing during learning; if the weights were to remain fixed, then the expected values of the target policy would be incorrect, possibly introducing other problems. Some newer offline RL algorithms such as Implicit Q-Learning (IQL, <a href="https://arxiv.org/abs/2110.06169" rel="nofollow noreferrer">paper</a>) attempt to circumvent this issue by using SARSA-style updates during training which do not query unseen state-action pairs, but there is no guarantee that the final extracted policy will not query actions that the behavior policy would have refrained from choosing, especially if function approximation is used.</p>
  <p>For further study, note that the survey you linked discusses a few other considerations regarding importance sampling for ORL, especially in Section 3.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-27T22:43:49.203Z
Answers.LastActivityDate: 2024-08-29T16:43:44.910Z
Answers.LastEditDate: 2024-08-29T16:43:44.910Z
Answers.UserDisplayName: DeepQZero
Body: <p>In offline RL we are usually equipped with a dataset, often also called Replay Buffer, that contains transitions in an episode, that are created by some behavior policy. This behavior policy could either be random, or could also be optimized with something like SAC.</p>
  <p>Generally, the goal of offline RL is to train a target policy on that dataset, that outperforms the behavior policy (like the random one or the policy trained with SAC): <em>'In offline RL, the whole point is to learn a policy that does something differently (presumably better) from the pattern of behavior observed in the dataset D.'</em> (<a href="https://arxiv.org/abs/2005.01643" rel="nofollow noreferrer">https://arxiv.org/abs/2005.01643</a>)</p>
  <p>One of the issues that come with off-policy and offline learning is the learning of a q-function with (action, state) pairs that come from the replay buffer (i.e. a mix of behavior policies) and (action, state) pairs that are sampled from the target policy which we are trying to learn. To be more precise, consider the loss of the q-function in SAC, which is usually the Mean Squared Error between the q-value of a state action pair (from the buffer) and a q-value of a <strong>next</strong> state action pair, where the action is not from the buffer, but from the target policy</p>
  <p>Thus, we have an action distribution from the behavior policy, and an action distribution from the target policy when learning the q-function. If both differ a lot, we can a pretty bad approximation of the q-values, hence we want to keep the target policy close to the behavior policy: <em>The fundamental challenge with making such counterfactual queries is distributional shift: while our function approximator (policy, value function, or model) might be trained under one distribution, it will be evaluated on a different distribution, due both to the change in visited states for the new policy and, more subtly, by the act of maximizing the expected return</em> (<a href="https://arxiv.org/abs/2005.01643" rel="nofollow noreferrer">https://arxiv.org/abs/2005.01643</a>)</p>
  <p>One way to handle this, is to keep the target policy close to the behavior policy by regularizing, for example by using a KL divergence penalty. So when the target policy deviates too much from the behavior one, it gets a penalty for the learning objective.</p>
  <p>Another way, if I understood the concept of IS correctly, would be to introduce importance sampling (only works for multi-steps algorithms though, since we cannot compute the is ratio for single steps) to estimate the expected values from samples that are drawn from the behavior policy w.r.t to the target policy. This would keep the distribution close to the target policy, in contrast to the policy regularization approach, which keeps the distribution close to the behavior policy.</p>
  <ol>
  <li><p>Are both assumptions correct?</p>
  </li>
  <li><p>Since I only see the first method used, what is the disadvantage of the second approach?</p>
  </li>
  </ol>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-05-09T15:56:21.867Z
Comments.Text: I'm not familiar with "policy regularization". It may only apply for certain RL methods. Could you please provide a link to the approach you want to compare with importance sampling? It may also help to explain what "the distribution" means to you, since I think there is some misunderstanding here that will contribute to any answer.
Comments.UserDisplayName: Neil Slater
Tags: <reinforcement-learning><probability-distribution><off-policy-methods><importance-sampling><offline-reinforcement-learning>
Title: How does Importance Sampling compare against Policy Regularization in Offline RL?
UserDisplayName: kklaw
ThreadText: # How does Importance Sampling compare against Policy Regularization in Offline RL?
  
  (Asked by: username_0 on 2024-05-08)
  
  In offline RL we are usually equipped with a dataset, often also called Replay Buffer, that contains transitions in an episode, that are created by some behavior policy. This behavior policy could either be random, or could also be optimized with something like SAC.
  
  Generally, the goal of offline RL is to train a target policy on that dataset, that outperforms the behavior policy (like the random one or the policy trained with SAC): *'In offline RL, the whole point is to learn a policy that does something differently (presumably better) from the pattern of behavior observed in the dataset D.'* (<https://arxiv.org/abs/2005.01643>)
  
  One of the issues that come with off-policy and offline learning is the learning of a q-function with (action, state) pairs that come from the replay buffer (i.e. a mix of behavior policies) and (action, state) pairs that are sampled from the target policy which we are trying to learn. To be more precise, consider the loss of the q-function in SAC, which is usually the Mean Squared Error between the q-value of a state action pair (from the buffer) and a q-value of a **next** state action pair, where the action is not from the buffer, but from the target policy
  
  Thus, we have an action distribution from the behavior policy, and an action distribution from the target policy when learning the q-function. If both differ a lot, we can a pretty bad approximation of the q-values, hence we want to keep the target policy close to the behavior policy: *The fundamental challenge with making such counterfactual queries is distributional shift: while our function approximator (policy, value function, or model) might be trained under one distribution, it will be evaluated on a different distribution, due both to the change in visited states for the new policy and, more subtly, by the act of maximizing the expected return* (<https://arxiv.org/abs/2005.01643>)
  
  One way to handle this, is to keep the target policy close to the behavior policy by regularizing, for example by using a KL divergence penalty. So when the target policy deviates too much from the behavior one, it gets a penalty for the learning objective.
  
  Another way, if I understood the concept of IS correctly, would be to introduce importance sampling (only works for multi-steps algorithms though, since we cannot compute the is ratio for single steps) to estimate the expected values from samples that are drawn from the behavior policy w.r.t to the target policy. This would keep the distribution close to the target policy, in contrast to the policy regularization approach, which keeps the distribution close to the behavior policy.
  
  1. Are both assumptions correct?
  2. Since I only see the first method used, what is the disadvantage of the second approach?
  
  **Tags:** reinforcement-learning, probability-distribution, off-policy-methods, importance-sampling, offline-reinforcement-learning
  > **Comments:**
  > **username_1**: I'm not familiar with "policy regularization". It may only apply for certain RL methods. Could you please provide a link to the approach you want to compare with importance sampling? It may also help to explain what "the distribution" means to you, since I think there is some misunderstanding here that will contribute to any answer.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2024-08-27. Score: 0
  
  > One way to handle this, is to keep the target policy close to the
  > behavior policy by regularizing, for example by using a KL divergence
  > penalty. So when the target policy deviates too much from the behavior
  > one, it gets a penalty for the learning objective.
  
  Regularizing the target policy to be close to the behavior policy has been done with some success in previous works (e.g. see Related Work section of the Conservative Q-Learning [paper](https://arxiv.org/abs/2006.04779)). The regularizer acts as a safeguard by preventing unrealistically high queried values of unseen state-action pairs to heavily influence the expected values of the target policy in the bootstrapping update. Since you have seen this method used before, I will not expand further.
  
  > Another way, if I understood the concept of IS correctly, would be to
  > introduce importance sampling to estimate the expected values from
  > samples that are drawn from the behavior policy w.r.t to the target
  > policy. This would keep the distribution close to the target
  > policy...
  
  You are correct in that importance sampling will estimate the expected values of the target policy from samples drawn from the behavior policy. However, importance sampling does not act as a safeguard as described previously. Specifically, implementing a reweighting scheme such as importance sampling when calculating the expected values does not prevent the agent from querying unseen state-action pairs. If these queried values are unrealistically high, then the target policy will learn to take those actions more often. This will result in an increase of the importance sampling weights corresponding to those state-action pairs, which will ultimately result in unrealistically high expected values of the target policy. From another point of view, the importance sampling weights for the state-action pairs with unrealistically high queried values may start small, but there is no safeguard against the weights increasing during learning; if the weights were to remain fixed, then the expected values of the target policy would be incorrect, possibly introducing other problems. Some newer offline RL algorithms such as Implicit Q-Learning (IQL, [paper](https://arxiv.org/abs/2110.06169)) attempt to circumvent this issue by using SARSA-style updates during training which do not query unseen state-action pairs, but there is no guarantee that the final extracted policy will not query actions that the behavior policy would have refrained from choosing, especially if function approximation is used.
  
  For further study, note that the survey you linked discusses a few other considerations regarding importance sampling for ORL, especially in Section 3.
  
  
  ---
  
  