Bandits for BMO Functions

We study the bandit problem where the underlying expected reward is a Bounded Mean Oscillation (BMO) function. BMO functions are allowed to be discontinuous and unbounded, and are useful in modeling signals with infinities in the do-main. We develop a toolset for BMO bandits, and provide an algorithm that can achieve poly-log $δ$-regret -- a regret measured against an arm that is optimal after removing a $δ$-sized portion of the arm space.

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