As one of the comments below the article states, the probabilistic alternative to epsilon-greedy is worth exploring ad well. Take the "bayesian bandit", which is not much more complex but a lot more powerful. If you crave more bandits: https://jamesrledoux.com/algorithms/bandit-algorithms-epsilo...
In my experience, obsessing on the best decision strategy is the biggest honeypot for engineers implementing MAB. Epsilon-greedy is very easy to implement and you probably don't need anything more. Thompson sampling is a pain in the butt, for not much gain.