Towards Macro-AUC oriented Imbalanced Multi-Label Continual Learning

TL;DR

This work tackles Macro-AUC optimization in imbalanced Multi-Label Continual Learning (MLCL) by proposing a memory replay-based framework. It introduces Reweighted Label-Distribution-Aware Margin (RLDAM), which integrates reweighting with label-distribution-aware margins to handle per-label class imbalance, and a memory updating strategy called Weight Retain Updating (WRU) to preserve the original dataset’s positive/negative ratios in memory. The authors provide theoretical generalization bounds for RLDAM in batch MLL and extend these insights to MLCL with memory replay, aided by a fractional Rademacher complexity analysis and optimal margin considerations. Empirically, the method demonstrates superior Macro-AUC performance on C-PASCAL-VOC, C-MSCOCO, and C-NUS-WIDE against strong baselines, with robust behavior across memory sizes and clear ablations of each component’s impact.

Abstract

In Continual Learning (CL), while existing work primarily focuses on the multi-class classification task, there has been limited research on Multi-Label Learning (MLL). In practice, MLL datasets are often class-imbalanced, making it inherently challenging, a problem that is even more acute in CL. Due to its sensitivity to imbalance, Macro-AUC is an appropriate and widely used measure in MLL. However, there is no research to optimize Macro-AUC in MLCL specifically. To fill this gap, in this paper, we propose a new memory replay-based method to tackle the imbalance issue for Macro-AUC-oriented MLCL. Specifically, inspired by recent theory work, we propose a new Reweighted Label-Distribution-Aware Margin (RLDAM) loss. Furthermore, to be compatible with the RLDAM loss, a new memory-updating strategy named Weight Retain Updating (WRU) is proposed to maintain the numbers of positive and negative instances of the original dataset in memory. Theoretically, we provide superior generalization analyses of the RLDAM-based algorithm in terms of Macro-AUC, separately in batch MLL and MLCL settings. This is the first work to offer theoretical generalization analyses in MLCL to our knowledge. Finally, a series of experimental results illustrate the effectiveness of our method over several baselines. Our codes are available at https://github.com/ML-Group-SDU/Macro-AUC-CL.

Figures (4)

• Figure 1: The comparison of training curves between our method and ER on C-PASCAL-VOC.
• Figure 2: The comparison of overall test performances (test on all tasks after learning each single task) between our method and ER on C-PASCAL-VOC.
• Figure 3: Imbalance statistics of samples of each class in three tasks in C-MSCOCO.
• Figure 4: The effect of hyper-parameter $\lambda$ to our RLDAM loss on C-PASCAL-VOC.

Theorems & Definitions (28)

• Theorem 1: Learning guarantee of RLDAM-based algorithm with WRU in MLCL, full proof in Appendix C
• Remark
• Theorem 2: Learning guarantee of RLDAM-based algorithm in batch MLL, full proof in Appendix \ref{['sec_app:proof_theorem1']}
• Definition 1: The fractional Rademacher complexity of the loss space, Definition 3 in wu2023towards
• Theorem 3: The base theorem of Macro-AUC, Theorem 1 in wu2023towards
• Definition 2: The fractional Rademacher complexity of the hypothesis space w.r.t. variant of reweighted univariate losses
• Lemma 1: The upper bound of fractional Rademacher complexity of kernel-based hypothesis space w.r.t. variant of reweighted univariate losses
• Lemma 2: A new contraction inequality for the RLDAM loss ${\mathcal{L}}_{\mathtt{RM}}$
• proof
• Theorem 3: Learning guarantee of RLDAM-based algorithm in batch MLL, full proof in Appendix \ref{['sec_app:proof_theorem1']}