Comparing Pointwise and Listwise Objective Functions for Random-Forest-Based Learning-to-Rank

Current random-forest (RF)-based learning-to-rank (LtR) algorithms use a classification or regression framework to solve the ranking problem in a pointwise manner. The success of this simple yet effective approach coupled with the inherent parallelizability of the learning algorithm makes it a strong candidate for widespread adoption. In this article, we aim to better understand the effectiveness of RF-based rank-learning algorithms with a focus on the comparison between pointwise and listwise approaches.

We introduce what we believe to be the first listwise version of an RF-based LtR algorithm. The algorithm directly optimizes an information retrieval metric of choice (in our case, NDCG) in a greedy manner. Direct optimization of the listwise objective functions is computationally prohibitive for most learning algorithms, but possible in RF since each tree maximizes the objective in a coordinate-wise fashion. Computational complexity of the listwise approach is higher than the pointwise counterpart; hence for larger datasets, we design a hybrid algorithm that combines a listwise objective in the early stages of tree construction and a pointwise objective in the latter stages. We also study the effect of the discount function of NDCG on the listwise algorithm.

Experimental results on several publicly available LtR datasets reveal that the listwise/hybrid algorithm outperforms the pointwise approach on the majority (but not all) of the datasets. We then investigate several aspects of the two algorithms to better understand the inevitable performance tradeoffs. The aspects include examining an RF-based unsupervised LtR algorithm and comparing individual tree strength. Finally, we compare the the investigated RF-based algorithms with several other LtR algorithms.