Multi-objective ranking with directions of preferences

Recently, gradient based multi-objective optimization methods have been developed to find models that are aligned with preference directions (MOO-PD) in machine learning community. Most of the methods are tuned and tested with multi-task learning problems in computer vision tasks with deep neural networks. While MOO-PD is useful in building a model with user specified MOO criteria, there is no existing work in the learning-to-rank (LTR) applications with gradient boosted ranking trees (GBRT), which is a popular method in LTR especially in production systems. Hence, there is no evidence
demonstrating that existing MOO-PD methods work well for LTR. In this paper, we apply several MOO-PD methods such as the Exact Pareto Optimal search, etc. to LTR. Further, to quantify model performance on MOO-PD, we propose a novel model evaluation metric, which is referred to as the maximum weighted loss. Through experiments, we reveal common challenges with MOO-PD methods, and propose a smoothing technique to address the challenges. The revised algorithms are shown to significantly improve the empirical performance on both public and proprietary datasets, indicating that we now have a realistic way to build MOO-PD models in GBRT, which may benefit many application use cases in practice.