Relevance and diversity are both crucial criteria for an effective search system. In this paper, we propose a unified learning framework for simultaneously optimizing both relevance and diversity. Specifically, the problem is formalized as a structural learning framework optimizing Diversity-Correlated Evaluation Measures (DCEM), such as ERR-IA, a-NDCG and NRBP. Within this framework, the discriminant function is defined to be a bi-criteria objective maximizing the sum of the relevance scores and dissimilarities (or diversity) among the documents. Relevance and diversity features are utilized to define the relevance scores and dissimilarities, respectively. Compared with traditional methods, the advantages of our approach lie in that: (1) Directly optimizing DCEM as the loss function is more fundamental for the task; (2) Our framework does not rely on explicit diversity information such as subtopics, thus is more adaptive to real application; (3) The representation of diversity as the feature-based scoring function is more flexible to incorporate rich diversity-based features into the learning framework. Extensive experiments on the public TREC datasets show that our approach significantly outperforms state-of-the-art diversification approaches, which validate the above advantages.
 In order to minimize redundancy and optimize coverage of multiple user interests, search engines and recommender systems aim to diversify their set of results. To date, these diversification mechanisms are largely hand-coded or relied on expensive training data provided by experts. To overcome this problem, we propose an online learning model and algorithms for learning diversified recommendations and retrieval functions from implicit feedback. In our model, the learning algorithm presents a ranking to the user at each step, and uses the set of documents from the presented ranking, which the user reads, as feedback. Even for imperfect and noisy feedback, we show that the algorithms admit theoretical guarantees for maximizing any submodular utility measure under approximately rational user behavior. In addition to the theoretical results, we find that the algorithm learns quickly, accurately, and robustly in empirical evaluations on two datasets. Algorithms for learning to rank Web documents usually assume a document's relevance is independent of other documents. This leads to learned ranking functions that produce rankings with redundant results. In contrast, user studies have shown that diversity at high ranks is often preferred. We present two online learning algorithms that directly learn a diverse ranking of documents based on users' clicking behavior. We show that these algorithms minimize abandonment, or alternatively, maximize the probability that a relevant document is found in the top k positions of a ranking. Moreover, one of our algorithms asymptotically achieves optimal worst-case performance even if users' interests change.