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In this work, we study sequential choice bandits with feedback. We proposebandit algorithms for a platform that personalizes users' experience tomaximize its rewards. For each action directed to a given user, the platform isgiven a positive reward, which is a non-decreasing function of the action, ifthis action is below the user's threshold. Users are equipped with a patiencebudget, and actions that are above the threshold decrease the user's patience.When all patience is lost, the user abandons the platform. The platformattempts to learn the thresholds of the users in order to maximize its rewards,based on two different feedback models describing the information patternavailable to the platform at each action. We define a notion of regret bydetermining the best action to be taken when the platform knows that the user'sthreshold is in a given interval. We then propose bandit algorithms for the twofeedback models and show that upper and lower bounds on the regret are of theorder of $\tilde{O}(N^{2/3})$ and $\tilde\Omega(N^{2/3})$, respectively, where$N$ is the total number of users. Finally, we show that the waiting time of anyuser before receiving a personalized experience is uniform in $N$.

Sequential Choice Bandits with Feedback for Personalizing users' experience