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Selecting the right web links for a website is important because appropriate links not only can provide high attractiveness but can also increase the website's revenue. In this work, we first show that web links have an intrinsic multi-level feedback structure. For example, consider a 2-level feedback web link: the 1st level feedback provides the Click-Through Rate (CTR) and the 2nd level feedback provides the potential revenue, which collectively produce the compound 2-level revenue. We consider the context-free links selection problem of selecting links for a homepage so as to maximize the total compound 2-level revenue while keeping the total 1st level feedback above a preset threshold. We further generalize the problem to links with n (n &#x2265; 2)-level feedback structure. The key challenge is that the links' multi-level feedback structures are unobservable unless the links are selected on the homepage. To our best knowledge, we are the first to model the links selection problem as a constrained multi-armed bandit problem and design an effective links selection algorithm by learning the links' multi-level structure with provable sub-linear regret and violation bounds. We uncover the multi-level feedback structures of web links in two real-world datasets. We also conduct extensive experiments on the datasets to compare our proposed LExp algorithm with two state-of-the-art context-free bandit algorithms and demonstrate that LExp algorithm is the most effective in links selection while satisfying the constraint.

Multi-level Feedback Web Links Selection Problem: Learning and Optimization