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Multi Armed Bandit for Continuous Rewards - Extended Question

This question is an extension to A continuous generalization of the binary bandit The Multi-Armed Bandit (MAB) Problem in general is described here: https://en.wikipedia.org/wiki/Multi-armed_bandit ...
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A continuous generalization of the binary bandit

There is plenty of reading out there about Bayesian (beta-binomial) multiarm bandits for 0/1 data, but I would like to extend this slightly. To give some context, suppose I have two webpages, A and ...