  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 $O(N \log^2 T)$.
