  Sequentially learning to place items in multi-position displays or lists is a
task that can be cast into the multiple-play semi-bandit setting. However, a
major concern in this context is when the system cannot decide whether the user
feedback for each item is actually exploitable. Indeed, much of the content may
have been simply ignored by the user. The present work proposes to exploit
available information regarding the display position bias under the so-called
Position-based click model (PBM). We first discuss how this model differs from
the Cascade model and its variants considered in several recent works on
multiple-play bandits. We then provide a novel regret lower bound for this
model as well as computationally efficient algorithms that display good
empirical and theoretical performance.
