Characterizing Bias in Post-Bandit Inference under Index Algorithms

Abstract:Bandit algorithms generate data for downstream inference, but adaptive sampling biases post-bandit sample means. We analyze this bias for stable index algorithms, including UCB1 and its generalizations, and derive sharp leading-order expressions for the sample-mean bias and expected $Z$-statistic. Our characterization reveals the algorithmic origin of bias through a key index-function-dependent quantity, which we term effective exploration rate. For example, under UCB1, the effective exploration rate is of order $\sqrt{\log T}$, and the standardized bias of any arm (that is not uniquely optimal) decays at the extremely slow rate $1/\sqrt{\log T}$. We also show how the choice of the index function affects both regret and bias, which reveals a regret-bias trade-off: more exploratory algorithm reduces bias but increases regret. Our sharp characterization for bias uses a novel empirical fluid approximation of the algorithm's sampling dynamics, which may be of independent interest.

Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML)

arXiv:2608.01069 [cs.LG]

(or arXiv:2608.01069v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.01069 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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