With a known optimality gap, streaming best-arm identification needs about log(n)/log log(n) passes with slightly sublinear memory, and O(log n) passes with a single arm of memory.
Single-pass streaming lower bounds for multi-armed bandits exploration with instance-sensitive sample complexity
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Nearly Tight Bounds for Exploration in Streaming Multi-armed Bandits with Known Optimality Gap
With a known optimality gap, streaming best-arm identification needs about log(n)/log log(n) passes with slightly sublinear memory, and O(log n) passes with a single arm of memory.