## Bandits for BMO Functions

### Tianyu Wang · Cynthia Rudin

Keywords: [ Reinforcement Learning ] [ Online Learning / Bandits ] [ Reinforcement Learning Theory ] [ Online Learning, Active Learning, and Bandits ]

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Abstract: 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 singularities in the domain. We develop a toolset for BMO bandits, and provide an algorithm that can achieve poly-log $\delta$-regret -- a regret measured against an arm that is optimal after removing a $\delta$-sized portion of the arm space.