The LambdaLoss Framework for Ranking Metric Optimization

How to optimize ranking metrics such as Normalized Discounted Cumulative Gain (NDCG) is an important but challenging problem, because ranking metrics are either flat or discontinuous everywhere, which makes them hard to be optimized directly. Among existing approaches, LambdaRank is a novel algorithm that incorporates ranking metrics into its learning procedure. Though empirically effective, it still lacks theoretical justification. For example, the underlying loss that LambdaRank optimizes for remains unknown until now. Due to this, there is no principled way to advance the LambdaRank algorithm further. In this paper, we present LambdaLoss, a probabilistic framework for ranking metric optimization. We show that LambdaRank is a special configuration with a well-defined loss in the LambdaLoss framework, and thus provide theoretical justification for it. More importantly, the LambdaLoss framework allows us to define metric-driven loss functions that have clear connection to different ranking metrics. We show a few cases in this paper and evaluate them on three publicly available data sets. Experimental results show that our metric-driven loss functions can significantly improve the state-of-the-art learning-to-rank algorithms.