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Here is one good overview:

http://www.cs.nyu.edu/~mohri/pub/bandit.pdf

"[...] ε-greedy is probably the simplest and the most widely used strategy to solve the bandit problem and was first described by Watkins [24]. The ε-greedy strategy consists of choosing a random lever with ε-frequency, and otherwise choosing the lever with the highest estimated mean, the estimation being based on the rewards observed thus far. ε must be in the open interval (0, 1) and its choice is left to the user. Methods that imply a binary distinction between exploitation (the greedy choice) and exploration (uniform probability over a set of levers) are known as semi-uniform methods."



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