Body: <p>I have been given a list of components, with various “contributions” (or weights) which put together in a weighted combination have a <strong>combined aggregate effect</strong>. I then have the task of <em>suggesting replacements</em> to some of the components with different weights,  which will maximise the overall aggregate effect.</p>
  <p>In <strong>Bayesian optimization</strong>, I would just be trying to find the right weights of each component that will maximize the objective function, but I am not aware of a model that can generate replacement suggestions in order to maximize the final aggregate objective function.</p>
  <p>For example, let’s say that you have parts that make up a car engine, and now you have to change a few parts to bring the overall cost down as you have a lower budget, but you want to keep the engine’s quality as close to the original one as possible. Then you have a few questions to answer like:</p>
  <ol>
  <li>What parts should be removed and replaced with what parts?</li>
  <li>How many new parts (weights) do we need?</li>
  <li>Is the weighted combination of parts able to satisfy our criteria and maximize it too?</li>
  </ol>
  <p>What ML model should I be looking into for such a task?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T01:58:07.987Z
Comments.Text: Are you looking for ML model to help you define your objective function for the combined aggregate effect? Is there any additional detail for the combined aggregate effect?
Comments.UserDisplayName: cinch
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:01:43.213Z
Comments.Text: @cinch No, I am looking for (possibly) a generative model that suggests replacements of components in such a way that it maximizes a fixed objective function.
Comments.UserDisplayName: user43464
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:10:43.630Z
Comments.Text: You need to first have reason to adjust weights in a (generative) way possibly in a continual learning ml model, is it because the operational data distribution will change over time? Generative models are not usually used to suggest adjustment based on some objective but generate data similar to its trained input distribution.
Comments.UserDisplayName: cinch
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:14:31.730Z
Comments.Text: This is not a continual learning setting where the data distribution changes over time. As an example, let’s say that you have parts that make up a car engine, and now for some reason you have to change a few parts to bring the overall cost down as you have a lower budget, but you want to keep the engine’s quality as close to the original one as possible. Then, what parts do you change/replace and with say what quantity of each part?
Comments.UserDisplayName: user43464
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:21:33.723Z
Comments.Text: This sounds like a Pareto optimization problem with a user defined cost structure, you need to add these details in OP with any other more details possible, no relation to Bayesian so far. Sounds like you would like a Bayesian update process to adjust those weights which is inconsistent with your cost-structured objective at least directly
Comments.UserDisplayName: cinch
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:35:43.263Z
Comments.Text: Are you suggesting a combination of a Pareto optimization problem for dealing with multiple objective functions, while using Bayesian Optimization to adjust the weights of the components to arrive at a Pareto optimal solution sooner?
Comments.UserDisplayName: user43464
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:45:44.667Z
Comments.Text: So, if I were to pose my problem as a multi-objective Pareto opt problem, where say I have tradeoffs like lowering the cost or adhering to some budget while maximizing some other utility, then how do I find the optimal “replacements” of parts and combine them in the most optimal manner to solve the problem? I would imagine my search space would explode if I had to manually change the parts and then see if they were optimal. Is there no way of exploring this space optimally? Also, would it help if I restricted the number of parts you could replace?
Comments.UserDisplayName: user43464
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-07-30T02:56:35.127Z
Comments.Text: Of course to simplify things you need to restrict the # of parts, with a clear cost structure for each part, you may first use the straightforward Linear Programming with total budget constraints as a baseline which may be good enough for your practical case. I don't see how Bayes and generative models help in your case since it's just one time adjustment not continual learning as you described.
Comments.UserDisplayName: cinch
Tags: <deep-learning><deep-rl><optimization><hyperparameter-optimization><bayesian-optimization>
Title: Combination of components to maximize a multi-criteria objective function
UserDisplayName: user43464
ThreadText: # Combination of components to maximize a multi-criteria objective function
  
  (Asked by: username_0 on 2024-07-30)
  
  I have been given a list of components, with various “contributions” (or weights) which put together in a weighted combination have a **combined aggregate effect**. I then have the task of *suggesting replacements* to some of the components with different weights, which will maximise the overall aggregate effect.
  
  In **Bayesian optimization**, I would just be trying to find the right weights of each component that will maximize the objective function, but I am not aware of a model that can generate replacement suggestions in order to maximize the final aggregate objective function.
  
  For example, let’s say that you have parts that make up a car engine, and now you have to change a few parts to bring the overall cost down as you have a lower budget, but you want to keep the engine’s quality as close to the original one as possible. Then you have a few questions to answer like:
  
  1. What parts should be removed and replaced with what parts?
  2. How many new parts (weights) do we need?
  3. Is the weighted combination of parts able to satisfy our criteria and maximize it too?
  
  What ML model should I be looking into for such a task?
  
  **Tags:** deep-learning, deep-rl, optimization, hyperparameter-optimization, bayesian-optimization
  
  > **Comments:**
  > **username_1**: Are you looking for ML model to help you define your objective function for the combined aggregate effect? Is there any additional detail for the combined aggregate effect?  
  > **username_0**: @username_1 No, I am looking for (possibly) a generative model that suggests replacements of components in such a way that it maximizes a fixed objective function.  
  > **username_1**: You need to first have reason to adjust weights in a (generative) way possibly in a continual learning ml model, is it because the operational data distribution will change over time? Generative models are not usually used to suggest adjustment based on some objective but generate data similar to its trained input distribution.  
  > **username_0**: This is not a continual learning setting where the data distribution changes over time. As an example, let’s say that you have parts that make up a car engine, and now for some reason you have to change a few parts to bring the overall cost down as you have a lower budget, but you want to keep the engine’s quality as close to the original one as possible. Then, what parts do you change/replace and with say what quantity of each part?  
  > **username_1**: This sounds like a Pareto optimization problem with a user defined cost structure, you need to add these details in OP with any other more details possible, no relation to Bayesian so far. Sounds like you would like a Bayesian update process to adjust those weights which is inconsistent with your cost-structured objective at least directly  
  > **username_0**: Are you suggesting a combination of a Pareto optimization problem for dealing with multiple objective functions, while using Bayesian Optimization to adjust the weights of the components to arrive at a Pareto optimal solution sooner?  
  > **username_0**: So, if I were to pose my problem as a multi-objective Pareto opt problem, where say I have tradeoffs like lowering the cost or adhering to some budget while maximizing some other utility, then how do I find the optimal “replacements” of parts and combine them in the most optimal manner to solve the problem? I would imagine my search space would explode if I had to manually change the parts and then see if they were optimal. Is there no way of exploring this space optimally? Also, would it help if I restricted the number of parts you could replace?  
  > **username_1**: Of course to simplify things you need to restrict the # of parts, with a clear cost structure for each part, you may first use the straightforward Linear Programming with total budget constraints as a baseline which may be good enough for your practical case. I don't see how Bayes and generative models help in your case since it's just one time adjustment not continual learning as you described.  
  
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  ## 0 answers
  
  