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 $Omega(frac{N log T}{ log log T})$. In the fixed-horizon setting, our algorithm FH-DUCB incurs $O(N log log T)$ 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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