Single-index bandits have optimal regret of order T^{2/3} via a two-phase algorithm that estimates the index direction with a Stein estimator then applies UCB on a grid.
Nonparametric bandits with single-index rewards: Optimality and adaptivity.arXiv preprint arXiv:2512.24669
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Optimal Regret for Single Index Bandits
Single-index bandits have optimal regret of order T^{2/3} via a two-phase algorithm that estimates the index direction with a Stein estimator then applies UCB on a grid.