Stochastic AUC Maximization with Deep Neural Networks

TL;DR

This paper extends stochastic AUC maximization to deep neural networks, proposing new algorithms under the Polyak-ojasiewicz condition that improve convergence and effectiveness for imbalanced data classification.

Contribution

It introduces a novel non-convex min-max formulation for deep neural network-based stochastic AUC maximization and develops faster algorithms leveraging the PL condition.

Findings

Proposed algorithms achieve faster convergence rates.

Experimental results validate the effectiveness of the methods.

Algorithms outperform existing approaches in imbalanced data tasks.

Abstract

Stochastic AUC maximization has garnered an increasing interest due to better fit to imbalanced data classification. However, existing works are limited to stochastic AUC maximization with a linear predictive model, which restricts its predictive power when dealing with extremely complex data. In this paper, we consider stochastic AUC maximization problem with a deep neural network as the predictive model. Building on the saddle point reformulation of a surrogated loss of AUC, the problem can be cast into a {\it non-convex concave} min-max problem. The main contribution made in this paper is to make stochastic AUC maximization more practical for deep neural networks and big data with theoretical insights as well. In particular, we propose to explore Polyak-\L{}ojasiewicz (PL) condition that has been proved and observed in deep learning, which enables us to develop new stochastic algorithms with even faster convergence rate and more practical step size scheme. An AdaGrad-style algorithm is also analyzed under the PL condition with adaptive convergence rate. Our experimental results demonstrate the effectiveness of the proposed algorithms.