Questions tagged [bellman-equations]

For questions related to the Bellman equations in the context of reinforcement learning (and other artificial intelligence subfields).

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77 views

Are these two definitions of the state-action value function equivalent?

I have been reading the Sutton and Barto textbook and going through David Silvers UCL lecture videos on YouTube and have a question on the equivalence of two forms of the state-action value function ...
1
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1answer
19 views

How are the Bellman optimality equations and minimax related?

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). ...
3
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2answers
71 views

What is the proof that policy evaluation converges to the optimal solution?

Although I know how the algorithm of iterative policy evaluation using dynamic programming works, I am having a hard time realizing how it actually converges. It appeals to intuition that, with each ...
2
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2answers
69 views

Why can the Bellman equation be turned into an update rule?

In chapter 4.1 of Sutton's book, the Bellman equation is turned into an update rule by simply changing the indices of it. How is it mathematically justified? I didn't quite get the initiation of why ...
2
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2answers
41 views

Why is there an expectation sign in the Bellman equation?

In chapter 3.5 of Sutton's book, the value function is defined as: Can someone give me some clarification about why there is the expectation sign behind the entire equation? Considering that the ...
6
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1answer
178 views

Why do Bellman equations indirectly create a policy?

I was watching a lecture on policy gradients and Bellman equations. And they say that a Bellman equation indirectly creates a policy, while the policy gradient directly learns a policy. Why is this?