Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning

11/23/2021
by   Zhenhuan Yang, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/25/2019

Stability and Optimization Error of Stochastic Gradient Descent for Pairwise Learning

In this paper we study the stability and its trade-off with optimization...
research
09/09/2022

Differentially Private Stochastic Gradient Descent with Low-Noise

In this paper, by introducing a low-noise condition, we study privacy an...
research
11/09/2021

Learning Rates for Nonconvex Pairwise Learning

Pairwise learning is receiving increasing attention since it covers many...
research
02/20/2023

Stability-based Generalization Analysis for Mixtures of Pointwise and Pairwise Learning

Recently, some mixture algorithms of pointwise and pairwise learning (PP...
research
08/17/2021

Stability and Generalization for Randomized Coordinate Descent

Randomized coordinate descent (RCD) is a popular optimization algorithm ...
research
06/09/2022

What is a Good Metric to Study Generalization of Minimax Learners?

Minimax optimization has served as the backbone of many machine learning...
research
05/31/2023

Optimal Estimates for Pairwise Learning with Deep ReLU Networks

Pairwise learning refers to learning tasks where a loss takes a pair of ...

Please sign up or login with your details

Forgot password? Click here to reset