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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

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  • $\begingroup$ What is the UCB algorithm? $\endgroup$
    – kodlu
    Commented Aug 10, 2023 at 20:59
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    $\begingroup$ Upper confidence bound in multi-armed bandit problem. $\endgroup$
    – Katan katalan
    Commented Aug 10, 2023 at 21:02
  • $\begingroup$ @katan could you post a reference or a place where it is used? $\endgroup$
    – user3483902
    Commented Aug 19, 2023 at 23:05
  • $\begingroup$ Because it's not necessary to assume that the reward distribution for each arm is normal? $\endgroup$
    – Karagounis Z
    Commented Aug 25, 2023 at 17:18

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