<p>Sutton and Barto explain it themselves <a href="http://incompleteideas.net/book/RLbook2020.pdf#page=136" rel="nofollow noreferrer">in section 5.9</a>. I post it with a bit of context. <strong>The equation you're looking for is 5.13</strong>.<a href="https://i.sstatic.net/3TSr8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3TSr8.png" alt="Excerpt from Section 5.9" /></a></p>

CC BY-SA 4.0
2021-08-31T18:05:23.123Z
2021-08-31T18:05:23.123Z
tnfru
<p>In Sutton &amp; Barto (2nd edition), the following is mentioned <a href="http://incompleteideas.net/book/RLbook2020.pdf#page=172" rel="nofollow noreferrer">on page 150 (p. 172 of the pdf), section 7.4</a>:</p>
<blockquote>
<p>the importance sampling ratio has expected value one (Section 5.9) and is uncorrelated with the estimate.</p>
</blockquote>
<p>How can we prove the importance sampling ratio is uncorrelated with the estimate?</p>

<proofs><off-policy-methods><sutton-barto><importance-sampling><model-free-methods>
How to prove importance sampling ratio is uncorrelated with action-value (or state-value) estimate?
user529295
# How to prove importance sampling ratio is uncorrelated with action-value (or state-value) estimate?

(Asked by: username_0 on 2021-08-20)

In Sutton & Barto (2nd edition), the following is mentioned [on page 150 (p. 172 of the pdf), section 7.4](http://incompleteideas.net/book/RLbook2020.pdf#page=172):

> the importance sampling ratio has expected value one (Section 5.9) and is uncorrelated with the estimate.

How can we prove the importance sampling ratio is uncorrelated with the estimate?

**Tags:** proofs, off-policy-methods, sutton-barto, importance-sampling, model-free-methods


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## 1 answers

### Answer by username_1 on 2021-08-31. Score: 1

Sutton and Barto explain it themselves [in section 5.9](http://incompleteideas.net/book/RLbook2020.pdf#page=136). I post it with a bit of context. **The equation you're looking for is 5.13**.[![Excerpt from Section 5.9](https://i.sstatic.net/3TSr8.png)](https://i.sstatic.net/3TSr8.png)


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