sequentially makes the decision on offered assortment. The performance of a dynamic policy is usually measured by the *regret*, which is defined as the gap between the expected revenue generated by the policy and the oracle expected revenue when $\theta_0$ (and thus the mean utilizes) is known as a priori.

The first contribution of the paper is the construction of an upper confidence bound (UCB) policy. Our UCB policy is based on the maximum likelihood estimator (MLE) and thus is named MLE-UCB. Although UCB has been a well-known technique for bandit problems, how to adopt this high-level idea to solve a problem with specific structures certainly requires technical innovations (e.g., how to build a confidence interval varies from one problem to another). In particular, our MLE-UCB contains two stages. The first stage is a *pure exploration stage* in which assortments are randomly offered and a *“pilot MLE”* is computed based on the observed purchase actions. As we will show in Lemma \[lem:pilot\], this pilot estimator serves as a good initial estimator of $\theta_0$. After the exploration phase, the MLE-UCB enters the *simultaneous learning and decision-making phase*. We carefully construct an upper confidence bound of the expected revenue when offering an 