Multinomial Logit Bandit with Low Switching Cost
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We study multinomial logit bandit with limited adaptivity, where the algorithms change their exploration actions as infrequently as possible when achieving almost optimal minimax regret. We propose two measures of adaptivity: the assortment switching cost and the more fine-grained item switching cost. We present an anytime algorithm (AT-DUCB) with O(N log T) assortment switches, almost matching the lower bound Ω(N log T/loglog T). In the fixed-horizon setting, our algorithm FH-DUCB incurs O(N loglog T) assortment switches, matching the asymptotic lower bound. We also present the ESUCB algorithm with item switching cost O(N log^2 T).
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