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This document contains proofs of theorems related to regret characterizations for instrument-armed bandits. It begins by proving that the expected cumulative contextual regret of an instrument-armed bandit algorithm is lower bounded by pminT, where pmin is the minimum probability of pulling any sub-optimal arm. It then proves that the expected cumulative regret of such an algorithm is O(T) by showing the instrument transfer and contextual regrets are each O(T). Finally, it provides proofs of auxiliary lemma

Author

Anonymous v3yZFLQ

Language

EN