<p>In UCB algorithm, to drive the confidence set for unknown parameters we use Hoeffding inequality. I am wondering why we don't use Normal distribution instead which is much simpler to work with. Based on the central limit theorem, when the sample size increases, we can approximate the sample mean distribution with Normal distribution. So, it won't have much error using this approximation.</p>
<p>Thanks</p>

CC BY-SA 4.0
2023-08-10T20:59:20.003Z
What is the UCB algorithm?
kodlu
CC BY-SA 4.0
2023-08-10T21:02:49.207Z
Upper confidence bound in multi-armed bandit problem.
Katan katalan
CC BY-SA 4.0
2023-08-19T23:05:04.340Z
@katan could you post a reference or a place where it is used?
user3483902
CC BY-SA 4.0
2023-08-25T17:18:17.047Z
Because it's not necessary to assume that the reward distribution for each arm is normal?
Karagounis Z
<lg.learning><online-learning>
Why do we use Hoeffding inequality in UCB approach to drive the confidence set in multi-armed bandit problem?
Katan katalan
# Why do we use Hoeffding inequality in UCB approach to drive the confidence set in multi-armed bandit problem?

(Asked by: username_0 on 2023-08-10)

In UCB algorithm, to drive the confidence set for unknown parameters we use Hoeffding inequality. I am wondering why we don't use Normal distribution instead which is much simpler to work with. Based on the central limit theorem, when the sample size increases, we can approximate the sample mean distribution with Normal distribution. So, it won't have much error using this approximation.

Thanks

**Tags:** lg.learning, online-learning

> **Comments:**
> **username_1**: What is the UCB algorithm?  
> **username_0**: Upper confidence bound in multi-armed bandit problem.  
> **username_2**: @katan could you post a reference or a place where it is used?  
> **username_3**: Because it's not necessary to assume that the reward distribution for each arm is normal?  

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## 0 answers

