Answers.Body: <p>Extracting a joint PDF just means that you create a model that models the behavior of several variables combined instead of in isolation. </p>
  
  <p>If these variables aren't independent and your loss functions is influenced by all of them, you obviously have to learn this joint PDF to minimize your loss. </p>
  
  <p>So I don't see this statement as particularly mysterious. </p>
  
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Answers.CreationDate: 2020-03-27T16:07:48.343Z
Answers.Text: The question is not "how can the joint distribution be useful in general", but "_how a Joint PDF would help with the "Optimal Stochastic Control of a Loss Function"_", although this answer may also answer the original question, if you are familiar with optimal stochastic control, etc.
Answers.UserDisplayName: nbro
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Answers.CreationDate: 2020-03-28T12:05:06.700Z
Answers.Text: @nbro yes that's exactly it. I'm wondering about the procedure by which modeling a joint PDF separately would help with the Optimal Stochastic Control of a Loss Function. I'm just learning RL so I'm sure that's where the confusion comes from.
Answers.UserDisplayName: Metrician
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-03-30T13:16:44.130Z
Answers.Text: From where do you get the "separately"?
Answers.UserDisplayName: BlindKungFuMaster
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Answers.CreationDate: 2020-03-27T15:57:55.433Z
Answers.LastActivityDate: 2020-03-27T15:57:55.433Z
Answers.UserDisplayName: BlindKungFuMaster
Body: <p>I stumbled upon a job offer from a company that was looking for someone who was good with Reinforcement Learning (applied to finance) and something in their offer caught my eye. It goes something like this:</p>
  
  <blockquote>
    <p>We want you to be able to study the price dynamic (of a stock I suppose) and its evolution in order to extract a Joint PDF that will be used in the Optimal Stochastic Control of a Loss Function (or gain)</p>
  </blockquote>
  
  <p>The thing is I understand what each of these things mean and how they are used separately (from my background in Control theory &amp; dynamical systems) and I worked with fitting Joint PDFs and Copulas before, but I don't understand how a Joint PDF would help with the "Optimal Stochastic Control of a Loss Function" ? Thanks.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-27T14:41:00.910Z
Comments.Text: Yes but I'm by no means an expert. I'm still trying to learn about it
Comments.UserDisplayName: Metrician
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-28T12:08:00.407Z
Comments.Text: Yes I'm aware of that but I'm not clear on the in-depth procedures as I'm still just getting started with RL. I was wondering about how would modeling a Joint PDF separately be used in the optimal stochastic control of the Loss Function. The exact procedure I mean
Comments.UserDisplayName: Metrician
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-28T12:47:32.730Z
Comments.Text: Oh I see. I didn't think they meant the joint PDF of rewards, usually in finance the Joint is computed using the price movement relative to other explanatory variables that's why I was confused. This makes more sense. Thanks a lot for the wealth of information you just gave me ! That'll keep me busy digging through it for days. Thanks also for the book and the chatroom. I'll definitely make sure to join.
Comments.UserDisplayName: Metrician
Tags: <reinforcement-learning><probability-distribution><control-theory>
Title: What does a joint probability density function have to do with Stochastic Optimal Control and Reinforcement Learning?
UserDisplayName: Metrician
ThreadText: # What does a joint probability density function have to do with Stochastic Optimal Control and Reinforcement Learning?
  
  (Asked by: username_0 on 2020-03-27)
  
  I stumbled upon a job offer from a company that was looking for someone who was good with Reinforcement Learning (applied to finance) and something in their offer caught my eye. It goes something like this:
  
  > We want you to be able to study the price dynamic (of a stock I suppose) and its evolution in order to extract a Joint PDF that will be used in the Optimal Stochastic Control of a Loss Function (or gain)
  
  The thing is I understand what each of these things mean and how they are used separately (from my background in Control theory & dynamical systems) and I worked with fitting Joint PDFs and Copulas before, but I don't understand how a Joint PDF would help with the "Optimal Stochastic Control of a Loss Function" ? Thanks.
  
  **Tags:** reinforcement-learning, probability-distribution, control-theory
  
  > **Comments:**
  > **username_0**: Yes but I'm by no means an expert. I'm still trying to learn about it  
  > **username_0**: Yes I'm aware of that but I'm not clear on the in-depth procedures as I'm still just getting started with RL. I was wondering about how would modeling a Joint PDF separately be used in the optimal stochastic control of the Loss Function. The exact procedure I mean  
  > **username_0**: Oh I see. I didn't think they meant the joint PDF of rewards, usually in finance the Joint is computed using the price movement relative to other explanatory variables that's why I was confused. This makes more sense. Thanks a lot for the wealth of information you just gave me ! That'll keep me busy digging through it for days. Thanks also for the book and the chatroom. I'll definitely make sure to join.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-03-27. Score: 1
  
  Extracting a joint PDF just means that you create a model that models the behavior of several variables combined instead of in isolation.
  
  If these variables aren't independent and your loss functions is influenced by all of them, you obviously have to learn this joint PDF to minimize your loss.
  
  So I don't see this statement as particularly mysterious.
  
  > **Comments:**
  > **username_2**: The question is not "how can the joint distribution be useful in general", but "_how a Joint PDF would help with the "Optimal Stochastic Control of a Loss Function"_", although this answer may also answer the original question, if you are familiar with optimal stochastic control, etc.  
  > **username_0**: @username_2 yes that's exactly it. I'm wondering about the procedure by which modeling a joint PDF separately would help with the Optimal Stochastic Control of a Loss Function. I'm just learning RL so I'm sure that's where the confusion comes from.  
  > **username_1**: From where do you get the "separately"?  
  
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