Learning Optimal Tree Models under Beam Search

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Jingwei Zhuo, Ziru Xu, Wei Dai, Han Zhu, HAN LI, Jian Xu, Kun Gai


<p>Retrieving relevant targets from an extremely large target set under computation and time limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves in a tree hierarchy and associate tree nodes with trainable node-wise scorers, have attracted a lot of interests in tackling this challenge due to its logarithmic computational complexity in both training and testing. Tree-based deep models (TDMs) and probabilistic label trees (PLTs) are two kinds of representative tree models. Though achieving many practical successes, existing tree models still suffer from training-testing discrepancy: in testing they usually leverage beam search to retrieve targets from the tree, which is not considered in the training loss function. As a result, even the optimal node-wise scorers with respect to the training loss can lead to suboptimal retrieval results when they are used in testing to retrieve targets via beam search. In this paper, we take a first step towards understanding the discrepancy by developing the definition of Bayes optimality and calibration under beam search as general analyzing tools, and prove that neither TDMs nor PLTs are Bayes optimal under beam search. To eliminating the discrepancy, we propose a novel training loss function with a beam search based subsampling method for training Bayes optimal tree models under beam search. Experiments on both synthetic and real data verify our analysis and demonstrate the superiority of our methods.</p>