Here’s why I don’t like the term “multi-armed bandit” to describe the exploration-exploitation tradeoff of inference and decision analysis.
First, and less importantly, each slot machine (or “bandit”) only has one arm. Hence it’s many one-armed bandits, not one multi-armed bandit.
Second, the basic strategy in these problems is to play on lots of machines until you find out which is the best, and then concentrate your plays on that best machine. This all presupposes that either (a) you’re required to play, or (b) at least one of the machines has positive expected value. But with slot machines, they all have negative expected value for the player (that’s why they’re called “bandits”), and the best strategy is not to play at all. So the whole analogy seems backward to me.
Third, I find the “bandit” terminology obscure and overly cute. It’s an analogy removed at two levels from reality: the optimization problem is not really like playing slot machines, and slot machines are not actually bandits. It’s basically a math joke, and I’m not a big fan of math jokes.
So, no deep principles here, the “bandit” name just doesn’t work for me. I agree with Bob Carpenter about the iid part (although I do remember a certain scene from The Grapes of Wrath with a non-iid slot machine), but other than that, the analogy seems a bit off.
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