Paper:
Online Reciprocal Recommendation with Theoretical Performance Guarantees
A reciprocal recommendation problem is one where the goal of learning is not just to predict a user's preference towards a passive item (e.g., a book), but to recommend the targeted user on one side another user from the other side such that a mutual interest between the two exists. The problem thus is sharply different from the more traditional items-to-users recommendation, since a good match requires meeting the preferences at both sides. We initiate a rigorous theoretical investigation of the reciprocal recommendation task in a specific framework of sequential learning. We point out general limitations, formulate reasonable assumptions enabling effective learning and, under these assumptions, we design and analyze a computationally efficient algorithm that uncovers mutual likes at a pace comparable to that achieved by a clairvoyant algorithm knowing all user preferences in advance. Finally, we validate our algorithm against synthetic and real-world datasets, showing improved empirical performance over simple baselines.

Review:
The authors consider the problem of online reciprocal recommendation (ORR), where a recommendation is successful if it satisfies both parties.  The online reciprocal recommendation is of practical importance as it can model online systems for job-matching, online dating, roommate matching and so on.   The authors model ORR as a planted bipartite graph where the two parties form the two partites and edges are hidden.  A query is directional between partites and the system gets to place two queries u->v’ and v->u’ on each time slot, where u and v are randomly chosen by nature. Moreover, an edge uv is established iff both u->v and v->u queries are made.   Under this model, the authors investigate how many such edges can be established in T = o(n^2) rounds.  They present negative results when a planted graph is unrestricted. In particular, there are graphs where an oblivious algorithm is optimal.  Whereas, when the feedbacks are clusterable they provide an efficient algorithm, namely SMILE, that learn an order-wise optimal number of edges.    The paper also validates the theoretical guarantees by testing them on a real-world dataset.  Pros: * The author initiates a theoretical study of the practically important problem of online reciprocal recommendation. * The proposed model of the ORR is novel and allows for key structural insights.  The quantification of clustering using a notion of covering number is also interesting. * The author provides a negative result: without structural assumption learning is not possible. Specifically, an oblivious online matching strategy matches the best possible performance. * On the positive side the authors show that when the received feedback is clusterable then through joint cluster learning and user matching order-wise optimal learning is possible, i.e. the number of edges uncovered by SMILE is of the same order of an algorithm that knows the planted bipartite graph.  * The paper is well written and easy to follow.   Cons: * The model falls short in capturing the real system as it  * The problem is considered from a learning perspective, whereas the quality of recommendation is overlooked. It is unclear how the learning can be used to improve performance under the proposed model.  The authors do point out this shortcoming.   * The authors claim that the experimental results validate the model. However, in the results section, the authors preprocess the dataset to remove users that have few edges. The authors should defend their validity claim when such alterations are made.  * The definition of a match through the two directed edges seem cumbersome. The authors may consider a different description that can be generalized easily to non-binary ratings. * The proposed model is far from practical, such as binary preference. It is not clear whether the current insights will remain significant in such a setting. The author may consider commenting on that.