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arXiv Machine Learning By Yingying Fan, Yuxuan Han, Jinchi Lv, Xiaocong Xu, Zhengyuan Zhou

Allocation Stability and Wald Inference under Variance-Aware UCB

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The paper investigates when allocation stability is required for Gaussian inference in a two‑armed, fixed‑horizon variance‑aware UCB policy with bounded rewards that may change with the horizon. It establishes a precise criterion involving the reward gap and variances that determines whether the optimal‑arm count can be approximated deterministically with vanishing relative error, while noting that the suboptimal‑arm count is always stable. The authors prove that the ordinary Wald statistic for any fixed nonzero coefficient vector converges to a standard normal distribution provided the product of pull count and reward variance diverges for each arm; however, uniform Gaussian approximation over deterministic coefficient vectors holds only if the optimal‑arm count is stable. The analysis relies on a pathwise comparison with an auxiliary policy and joint limits for the rescaled optimal‑arm count and studentized sample‑mean errors.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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