Scalable Learning of Non-Decomposable Objectives
  Modern retrieval systems are often driven by an underlying machine learning model. The goal of such systems is to identify and possibly rank the few most relevant items for a given query or context. Thus, such systems are typically evaluated using a ranking-based performance metric such as the area under the precision-recall curve, the $F_\beta$ score, precision at fixed recall, etc. Obviously, it is desirable to train such systems to optimize the metric of interest.   In practice, due to the scalability limitations of existing approaches for optimizing such objectives, large-scale retrieval systems are instead trained to maximize classification accuracy, in the hope that performance as measured via the true objective will also be favorable. In this work we present a unified framework that, using straightforward building block bounds, allows for highly scalable optimization of a wide range of ranking-based objectives. We demonstrate the advantage of our approach on several real-life retrieval problems that are significantly larger than those considered in the literature, while achieving substantial improvement in performance over the accuracy-objective baseline. 
Elad ET. Eban, Mariano Schain, Alan Mackey, Ariel Gordon, Rif A.   Saurous, Gal Elidan
stat.ML cs.LG