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Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning
ZHENHUAN YANG · Yunwen Lei · Puyu Wang · Tianbao Yang · Yiming Ying

Thu Dec 09 04:30 PM -- 06:00 PM (PST) @

Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OGD) algorithm, where one needs to pair the current instance with a buffering set of previous instances with a sufficiently large size and therefore suffers from a scalability issue. In this paper, we propose simple stochastic and online gradient descent methods for pairwise learning. A notable difference from the existing studies is that we only pair the current instance with the previous one in building a gradient direction, which is efficient in both the storage and computational complexity. We develop novel stability results, optimization, and generalization error bounds for both convex and nonconvex as well as both smooth and nonsmooth problems. We introduce novel techniques to decouple the dependency of models and the previous instance in both the optimization and generalization analysis. Our study resolves an open question on developing meaningful generalization bounds for OGD using a buffering set with a very small fixed size. We also extend our algorithms and stability analysis to develop differentially private SGD algorithms for pairwise learning which significantly improves the existing results.

Author Information

ZHENHUAN YANG (State University of New York, Albany)
Yunwen Lei (University of Birmingham)

I am currently a Lecturer at School of Computer Science, University of Birmingham. Previously, I was a Humboldt Research Fellow at University of Kaiserslautern, a Research Assistant Professor at Southern University of Science and Technology, and a Postdoctoral Research Fellow at City University of Hong Kong. I obtained my PhD degree in Computer Science at Wuhan University in 2014.

Puyu Wang (City University of Hong Kong)
Tianbao Yang (The University of Iowa)
Yiming Ying (State University of New York at Albany)

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