UNCERTAINTY QUANTIFICATION OF RIEMANNIAN LOW-RANK TENSOR BANDITS WITH ROTATED ELIM- INATION

Low-rank tensor bandits model multi-dimensional online decision problems, such as joint user segment–product–channel selection in online advertising. Existing tensor bandit algorithms focus on reward maximization but do not adequately address uncertainty quantification. To fill this gap, we study an inferential tensor bandit framework with a low-rank reward tensor and adaptively generated, batched online data. Two challenges arise. First, low-regret policies may prematurely stop sampling actions relevant to the inferential target, leaving insufficient information in its direction. Second, the low-rank constraint introduces nonlinear estimation bias, whereas policy-dependent sampling distributions invalidate conventional inference methods. We propose Rotated Inferential Tensor Elimination (RITE), an online, batched non-contextual bandit algorithm with a fixed rotated-elimination rule for decisions and an evolving low-rank nuisance estimator for quantification. RITE combines spectral rotation, maximum-confidence-width exploration, and active-set elimination, and uses Riemannian capped inverse-propensity updates for low-rank estimation. For inference, it constructs a stabilized one-step debiasing estimator that simultaneously handles low-rank estimation error and adaptive sampling. Theoretically, we establish a nonasymptotic error bound for Riemannian low-rank estimation, prove asymptotic normality for the efficient inference, and derive a finite-time regret bound that preserves the typical order of tensor elimination while adding only the cost of target exploration. Simulations and an online advertising experiment show that RITE yields confidence intervals with near-nominal coverage while maintaining regret close to tensor elimination.