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.
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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.