Answers.Body: <p>They have similar philosophies, in the sense that minimax and algorithms based on the Bellman optimality equations are used to solve optimization problems, but they are also different because they solve different problems. </p>
  
  <p>Minimax (at least, the minimax version that I am aware of) is typically used to solve two-player games (e.g. chess, tic-tac-toe, etc.), while Bellman optimality equations (I assume you are referring to the Bellman equations that algorithms such as policy iteration are based on) do not assume the existence of two players (unless you consider the environment a player).</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-22T16:16:34.720Z
Answers.Text: Allright so the assumption of "two-players" sets them apart?
Answers.UserDisplayName: gfdsal
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-22T16:18:38.297Z
Answers.Text: @gfdsal I guess so (at least in most cases), but minimax may also be used in other context and I don't exclude the existence of "Bellman equations" for two-player games (I am just not aware of them right now).
Answers.UserDisplayName: nbro
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-22T15:31:40.523Z
Answers.LastActivityDate: 2020-04-22T15:37:32.380Z
Answers.LastEditDate: 2020-04-22T15:37:32.380Z
Answers.UserDisplayName: nbro
Body: <p>Is the philosophy between Bellman equations and minimax the same? </p>
  
  <p>Both the algorithms look at the full horizon and take into account potential gains (Bellman) and potential losses (minimax). </p>
  
  <p>However, do the two differ besides the obvious on the fact that Bellman equations use discounted potential rewards, while minimax deals with potential losses without the discount? Are these enough to say they are similar in philosophy or is are they dissimilar? If so, then in what sense?</p>
  
Tags: <reinforcement-learning><comparison><game-theory><minimax><bellman-equations>
Title: How are the Bellman optimality equations and minimax related?
UserDisplayName: gfdsal
ThreadText: # How are the Bellman optimality equations and minimax related?
  
  (Asked by: username_0 on 2020-04-22)
  
  Is the philosophy between Bellman equations and minimax the same?
  
  Both the algorithms look at the full horizon and take into account potential gains (Bellman) and potential losses (minimax).
  
  However, do the two differ besides the obvious on the fact that Bellman equations use discounted potential rewards, while minimax deals with potential losses without the discount? Are these enough to say they are similar in philosophy or is are they dissimilar? If so, then in what sense?
  
  **Tags:** reinforcement-learning, comparison, game-theory, minimax, bellman-equations
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-04-22. Score: 0 | Accepted answer
  
  They have similar philosophies, in the sense that minimax and algorithms based on the Bellman optimality equations are used to solve optimization problems, but they are also different because they solve different problems.
  
  Minimax (at least, the minimax version that I am aware of) is typically used to solve two-player games (e.g. chess, tic-tac-toe, etc.), while Bellman optimality equations (I assume you are referring to the Bellman equations that algorithms such as policy iteration are based on) do not assume the existence of two players (unless you consider the environment a player).
  
  > **Comments:**
  > **username_0**: Allright so the assumption of "two-players" sets them apart?  
  > **username_1**: @gfdsal I guess so (at least in most cases), but minimax may also be used in other context and I don't exclude the existence of "Bellman equations" for two-player games (I am just not aware of them right now).  
  
  ---
  
  