Questions tagged [bellman-operators]

For questions related to Bellman operators in the context of reinforcement learning.

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Why are the Bellman operators contractions?

In these slides, it is written \begin{align} \left\|T^{\pi} V-T^{\pi} U\right\|_{\infty} & \leq \gamma\|V-U\|_{\infty} \tag{9} \label{9} \\ \|T V-T U\|_{\infty} & \leq \gamma\|V-U\|_{\infty} \...
1 vote
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Off-policy Bellman Operators: Writing Operator and Weight Update Function for a 2-State System

I am studying for RL on my own and was trying to solve this question I came across. Write an operator function $T(w, \pi, \mu, l, g)$ that takes weights $w$, a target policy $\pi$, a behaviour policy ...
23 votes
1 answer

What is the Bellman operator in reinforcement learning?

In mathematics, the word operator can refer to several distinct but related concepts. An operator can be defined as a function between two vector spaces, it can be defined as a function where the ...
3 votes
1 answer

What do the terms 'Bellman backup' and 'Bellman error' mean?

Some RL literature use terms such as: 'Bellman backup' and 'Bellman error'. What do these terms refer to?
1 vote
1 answer

How to derive matrix form of the Bellman operators?

Reading the Retrace paper (Safe and efficient off-policy reinforcement learning) I saw they often use a matrix form of the Bellman operators, for example as in the picture below. How do we derive ...