  Optimizing the assortment of products to display to customers is a key to
increasing revenue for both offline and online retailers. To trade-off between
exploring customers' preference and exploiting customers' choices learned from
data, in this paper, by adopting the Multi-Nomial Logit (MNL) choice model to
capture customers' choices over products, we study the problem of optimizing
assortments over a planning horizon $T$ for maximizing the profit of the
retailer. To make the problem setting more practical, we consider both the
inventory constraint and the limited switches constraint, where the retailer
cannot use up the resource inventory before time $T$ and is forbidden to switch
the assortment shown to customers too many times. Such a setting suits the case
when an online retailer wants to dynamically optimize the assortment selection
for a population of customers. We develop an efficient UCB-like algorithm to
optimize the assortments while learning customers' choices from data. We prove
that our algorithm can achieve a sub-linear regret bound
$\tilde{O}\left(T^{1-\alpha/2}\right)$ if $O(T^\alpha)$ switches are allowed.
%, and our regret bound is optimal with respect to $T$. Extensive numerical
experiments show that our algorithm outperforms baselines and the gap between
our algorithm's performance and the theoretical upper bound is small.
