[论文解读] Joint Training of Deep Ensembles Fails Due to Learner Collusion

Alan Jeffares, Tennison Liu+2 more|arXiv (Cornell University)|Jan 26, 2023

Adversarial Robustness in Machine Learning被引用 4

一句话总结

本文表明，深度集成模型的联合训练因‘学习者共谋’（learner collusion）而失败，这是一种现象：基模型在预测空间中人为地夸大多样性以最小化集成损失，从而导致泛化性能下降。尽管优化了真实的集成目标，这种共谋行为反而使泛化误差大于独立训练，后者在实践中仍更有效。

ABSTRACT

Ensembles of machine learning models have been well established as a powerful method of improving performance over a single model. Traditionally, ensembling algorithms train their base learners independently or sequentially with the goal of optimizing their joint performance. In the case of deep ensembles of neural networks, we are provided with the opportunity to directly optimize the true objective: the joint performance of the ensemble as a whole. Surprisingly, however, directly minimizing the loss of the ensemble appears to rarely be applied in practice. Instead, most previous research trains individual models independently with ensembling performed post hoc. In this work, we show that this is for good reason - joint optimization of ensemble loss results in degenerate behavior. We approach this problem by decomposing the ensemble objective into the strength of the base learners and the diversity between them. We discover that joint optimization results in a phenomenon in which base learners collude to artificially inflate their apparent diversity. This pseudo-diversity fails to generalize beyond the training data, causing a larger generalization gap. We proceed to comprehensively demonstrate the practical implications of this effect on a range of standard machine learning tasks and architectures by smoothly interpolating between independent training and joint optimization.

研究动机与目标

• 调查为何联合优化深度集成模型的性能劣于独立训练，尽管前者是真实的集成目标。
• 识别联合训练集成模型中泛化性能差的根本原因，特别是人工多样性的作用。
• 正式将集成目标分解为单个模型性能与多样性项，揭示退化行为的机制。
• 通过实证方法验证学习者共谋在标准基准和架构上的存在及其影响。
• 探索潜在解决方案，如学习者丢弃（learner dropout），并展示其在缓解该问题上的局限性。

提出的方法

• 作者通过二阶泰勒展开，将联合集成损失分解为单个模型损失与多样性项，形式化了联合训练与独立训练目标之间的关系。
• 引入标量权重超参数 β，实现从独立训练（β=0）到完全联合优化（β=1）的平滑插值，从而实现对训练策略的受控分析。
• 多样性项被定义为联合训练与独立训练目标之间的差异，量化了学习者间分歧对整体损失的贡献。
• 学习者共谋被诊断为一种策略：基模型通过相互反向移动预测，以增加表观多样性，同时保持集成输出不变，从而利用多样性项。
• 在多个架构（ResNet-18、VGG）和数据集（CIFAR-10、SVHN）上进行实验，测量不同 β 值下的泛化误差、多样性得分与测试误差。
• 评估了一种基于丢弃的缓解策略：在每个训练批次中随机丢弃部分模型，以破坏共谋行为，但该方法因自举效应而降低性能。

Figure 2 : Diversity explosion. Test set diversity explodes relative to MSE across four datasets. We note two further empirical phenomena: (1) the non-linear relationship between $\beta$ and diversity which we discuss further in Appendix D and (2) the minimal effect diversity has on the test MSE on

实验结果

研究问题

• RQ1 为何联合训练深度集成模型无法泛化，尽管其优化了真实的集成目标？
• RQ2 与独立训练相比，联合训练集成模型性能退化的具体机制是什么？
• RQ3 基学习者之间的人为共谋在多大程度上可操纵集成目标中的多样性项？
• RQ4 在独立训练与联合训练之间不同插值水平下，泛化误差差距如何变化？
• RQ5 正则化技术如学习者丢弃能否有效缓解学习者共谋的负面影响？

主要发现

• 尽管优化了真实的集成目标，联合训练深度集成模型的泛化误差仍大于独立训练。
• 学习者共谋成为关键失败模式：基模型在不提升实际泛化能力的前提下，人为增加预测空间中的多样性。
• 实验表明，集成损失中的多样性项是联合训练与独立训练性能差异的主要驱动因素。
• 在 CIFAR-10 与 SVHN 上的实验表明，随着 β 增大至 1，性能单调下降，表明完全联合优化下的泛化性能更差。
• 学习者丢弃可减少共谋引发的多样性，但同时因自举效应削弱了单个模型，从而抵消了任何性能增益。
• 该现象在不同架构（ResNet-18、VGG）与数据集上均一致，表明其是联合集成训练中的根本性问题。

Figure 3 : Bias removal. The percentage of diversity explained by the most simple form of learner collusion across each dataset. In the region where learner collusion appears to occur ( $\beta\to 1$ ), a large proportion of the diversity can be explained by simple additive bias in the predictions.