Bayesian terminology for experiments I am learning about bayesian experimental design and confused about the "Bayesian" terminology. Multi-armed bandits are normally in the syllabus of bayesian experiments. But there are techniques like Thompson sampling which uses bayesian optimisation and there are also non-bayesian bandit algorithms.
So my question is:

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*Can experiments conducted using epsilon greedy bandit algorithms called bayesian experiment?

*Is bayesian optimisation different from bayesian experimental design?


The "Bayesian" in Bayesian optimization stems from the Bayesian updating of our beliefs about the shape of the function we are optimizing.
Imagine we want to minimize $f(x) \colon R^D \to R$.  We start with prior beliefs about the shape of $f$, let's call it $\hat{f}_0$. Then, we evaluate the target function at some point, say $x_1 \in R^D$. Now, we have learned about the value $f(x_1)$. With this new information, we update our beliefs about $\hat{f}_0$ via Bayes rule. We have new beliefs, $\hat{f}_1$, and we repeat.
Note that I said "we evaluate the target function at some point $x_1$". But the question is which point to choose? The study of various strategies of choosing these points is known as "Bayesian experimental design." Why Bayesian? Because based on the prior, $\hat{f}$.
