Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence

Zi-Hao Qiu, Quanqi Hu, Yongjian Zhong, Lijun Zhang, Tianbao Yang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:18122-18152, 2022.

Abstract

NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-qiu22a, title = {Large-scale Stochastic Optimization of {NDCG} Surrogates for Deep Learning with Provable Convergence}, author = {Qiu, Zi-Hao and Hu, Quanqi and Zhong, Yongjian and Zhang, Lijun and Yang, Tianbao}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {18122--18152}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/qiu22a/qiu22a.pdf}, url = {https://proceedings.mlr.press/v162/qiu22a.html}, abstract = {NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org.} }
Endnote
%0 Conference Paper %T Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence %A Zi-Hao Qiu %A Quanqi Hu %A Yongjian Zhong %A Lijun Zhang %A Tianbao Yang %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-qiu22a %I PMLR %P 18122--18152 %U https://proceedings.mlr.press/v162/qiu22a.html %V 162 %X NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org.
APA
Qiu, Z., Hu, Q., Zhong, Y., Zhang, L. & Yang, T.. (2022). Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:18122-18152 Available from https://proceedings.mlr.press/v162/qiu22a.html.

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