Yes - Satyen Kale, Rob Schapire, and I have a paper on this very problem, where we consider choosing "slates" of arms instead of individual arms. We consider the cases when position matters in the slate and when it doesn't. We also analyze both the experts MAB "contextual" model and the expertless setting.

Yes - Satyen Kale, Rob Schapire, and I have a recent paper (NIPS '10) on this very problem, where we consider choosing "slates" of arms instead of individual arms. We consider the cases when position matters in the slate and when it doesn't. We also analyze both the experts MAB "contextual" model and the expertless setting.