Online Collaborative-Filtering on Graphs

A common phenomena in modern recommendation systems is the use of feedback from one user to infer the `value' of an item to other users. This results in an exploration vs. exploitation trade-off, in which items of possibly low value have to be presented to users in order to ascertain their value. Existing approaches to solving this problem focus on the case where the number of items are small, or admit some underlying structure -- it is unclear, however, if good recommendation is possible when dealing with content-rich settings with unstructured content. We consider this problem under a simple natural model, wherein the number of items and the number of item-views are of the same order, and an `access-graph' constrains which user is allowed to see which item. Our main insight is that the presence of the access-graph in fact makes good recommendation possible -- however this requires the exploration policy to be designed to take advantage of the access-graph. Our results demonstrate the importance of `serendipity' in exploration, and how higher graph-expansion translates to a higher quality of recommendations; it also suggests a reason why in some settings, simple policies like Twitter's `Latest-First' policy achieve a good performance. From a technical perspective, our model presents a way to study exploration-exploitation tradeoffs in settings where the number of `trials' and `strategies' are large (potentially infinite), and more importantly, of the same order. Our algorithms admit competitive-ratio guarantees which hold for the worst-case user, under both finite-population and infinite-horizon settings, and are parametrized in terms of properties of the underlying graph. Conversely, we also demonstrate that improperly-designed policies can be highly sub-optimal, and that in many settings, our results are order-wise optimal.