The story
From one-armed bandit, by analogy with a gambler at a row of slot machines who has to decide how best to play them.
Etymology from Wiktionary, CC BY-SA 4.0.
multi-armed bandit
Today it means: An algorithm that allocates a fixed limited set of resources between competing alternative choices so as to maximize the expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or allocations are made. Full definition →