Unverified50% confidenceFactExact time
This universal lower bound delineates the boundary for kernel bandit algorithm design: the regret performance of any new algorithm cannot surpass Ω(√(Tγ_T/log T)).
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10/9/2026
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UnverifiedThe maximum information gain γ_T characterizes the upper limit on the information about the unknown function that an algorithm can obtain through observations in T rounds of interaction, and largely determines the difficulty boundary of the kernelized bandit problem.70% similarUnverifiedThe lower bound for the standard multi-armed bandit problem is O(√T), and ORUCB's extra log(T+1) factor stems from the complexity introduced by simultaneously learning the correction function.68% similarUnverifiedWhen using exact rational arithmetic, the bit length of intermediate rational numbers in the classical LLL algorithm can reach O(n·β) in the worst case, with an overall complexity of O(n⁵·β³) or even higher.63% similarUnverifiedNaively approximating the infinite-dimensional functional gradient causes the algorithm to converge to the wrong location, introducing systematic bias.62% similarUnverified在多臂老虎机理论中，纯粹的利用会导致遗憾的线性增长，而适度的探索能在长期实现对数级别的遗憾上界62% similar
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