Answers.Body: <p>There are multiple ways to structure a reward system to manage some form of homeostasis, i.e. where despite changes in external environment or forces acting against the agent, it takes action to maintain some important part of the state.</p>
  <p>The simplest would be to have +1 reward for each time step that the agent met the conditions that you want. This will still allow the agent to learn conservative behaviour well - e.g. if random forces might force your variable <span class="math-container">$y$</span> out of bounds, the agent will learn that having <span class="math-container">$y$</span> as a (possibly weighted) mid-point of <span class="math-container">$y_{max}, y_{min}$</span> would have the highest expected return and would prefer that without you have to more directly reward it.</p>
  <p>If your environment is not naturally episodic, you may want to use a discount factor <span class="math-container">$\gamma$</span> so that predicted return does not get very high, or use an average reward setting. Maintaining a stasis state can often be treated as either episodic or continuing though, so use whichever you are more comfortable for describing the problem overall.</p>
  <p>It might equally be viable to reward -1 for every time step spent outside bounds, or a reward based on distance from a target value with maybe a step function (e.g. an additional -1 for being outside bounds) depending on the agent meeting constraints or not.</p>
  <p>If the episode ends when constraints are not met (similar to CartPole toy environment), then the simple +1 reward per step is enough. The agent is effectively &quot;punished&quot; with a lower return if it cannot continue.</p>
  <p>In short, there might be a few bad choices for reward function in your case, but there are quite a few good options. I'd recommend to start simple, as per this answer's second paragraph. If you are not sure whether you have picked a good choice, then you should ask a new question with more details on the environment, your goals for the agent and the reward function that you are considering.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-25T11:54:30.833Z
Answers.LastActivityDate: 2024-08-25T11:54:30.833Z
Answers.UserDisplayName: Neil Slater
Body: <p>If I want the RL agent to keep the output in the range <span class="math-container">$[y_{min}, y_{max}]$</span>, what can be the optimal definition of a reward function for this purpose? By output we mean this: assume that the agent is controlling the position of something and we want this position to remain in [pos_min, pos_max].</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-08-25T00:50:29.603Z
Comments.Text: what exactly do you mean by output? Is the output an expected return or is it an action that the agent takes?
Comments.UserDisplayName: DeepQZero
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-08-25T01:06:16.140Z
Comments.Text: if that's the action space range, just use an appropriate activation function (something like $(tanh(f(x)+1)/2 \cdot (y_{max}-y_{min})+y_{min}$)
Comments.UserDisplayName: Alberto
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-08-25T10:37:59.570Z
Comments.Text: By output we mean this: assume that the agent is controlling the position of something and we want this position to remain in [pos_min, pos_max].
Comments.UserDisplayName: DSPinfinity
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-08-25T11:37:02.663Z
Comments.Text: How directly is the agent controlling this position? Specifically is the agent's output directly the position, or is the position the *result* of the agent's action as it is impacted by the environment? E.g. is the agent's action some motor forces or on/off switches for a machine?
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-08-25T11:57:05.980Z
Comments.Text: I have assumed in my answer that the agent's actions are not directly a choice of position, but something related to it such as choosing a force to apply or a speed etc.
Comments.UserDisplayName: Neil Slater
Tags: <reinforcement-learning>
Title: How to define a good reward function to keep output $y$ in the range $[y_{min}, y_{max}]$?
UserDisplayName: DSPinfinity
ThreadText: # How to define a good reward function to keep output $y$ in the range $[y_{min}, y_{max}]$?
  
  (Asked by: username_0 on 2024-08-24)
  
  If I want the RL agent to keep the output in the range $[y\_{min}, y\_{max}]$, what can be the optimal definition of a reward function for this purpose? By output we mean this: assume that the agent is controlling the position of something and we want this position to remain in [pos\_min, pos\_max].
  
  **Tags:** reinforcement-learning
  
  > **Comments:**
  > **username_1**: what exactly do you mean by output? Is the output an expected return or is it an action that the agent takes?  
  > **username_2**: if that's the action space range, just use an appropriate activation function (something like $(tanh(f(x)+1)/2 \cdot (y_{max}-y_{min})+y_{min}$)  
  > **username_0**: By output we mean this: assume that the agent is controlling the position of something and we want this position to remain in [pos_min, pos_max].  
  > **username_3**: How directly is the agent controlling this position? Specifically is the agent's output directly the position, or is the position the *result* of the agent's action as it is impacted by the environment? E.g. is the agent's action some motor forces or on/off switches for a machine?  
  > **username_3**: I have assumed in my answer that the agent's actions are not directly a choice of position, but something related to it such as choosing a force to apply or a speed etc.  
  
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  ## 1 answers
  
  ### Answer by username_3 on 2024-08-25. Score: 2 | Accepted answer
  
  There are multiple ways to structure a reward system to manage some form of homeostasis, i.e. where despite changes in external environment or forces acting against the agent, it takes action to maintain some important part of the state.
  
  The simplest would be to have +1 reward for each time step that the agent met the conditions that you want. This will still allow the agent to learn conservative behaviour well - e.g. if random forces might force your variable $y$ out of bounds, the agent will learn that having $y$ as a (possibly weighted) mid-point of $y\_{max}, y\_{min}$ would have the highest expected return and would prefer that without you have to more directly reward it.
  
  If your environment is not naturally episodic, you may want to use a discount factor $\gamma$ so that predicted return does not get very high, or use an average reward setting. Maintaining a stasis state can often be treated as either episodic or continuing though, so use whichever you are more comfortable for describing the problem overall.
  
  It might equally be viable to reward -1 for every time step spent outside bounds, or a reward based on distance from a target value with maybe a step function (e.g. an additional -1 for being outside bounds) depending on the agent meeting constraints or not.
  
  If the episode ends when constraints are not met (similar to CartPole toy environment), then the simple +1 reward per step is enough. The agent is effectively "punished" with a lower return if it cannot continue.
  
  In short, there might be a few bad choices for reward function in your case, but there are quite a few good options. I'd recommend to start simple, as per this answer's second paragraph. If you are not sure whether you have picked a good choice, then you should ask a new question with more details on the environment, your goals for the agent and the reward function that you are considering.
  
  
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