用方向反馈实现在线序数回归，效果接近全信息学习。
DFORD: Directional Feedback based Online Ordinal Regression Learning
- 基于左右方向反馈设计在线学习算法，平衡探索与利用。
- 理论证明期望遗憾为 $\mathcal{O}(\log T)$，且阈值顺序被保持。
- 适合标注成本高、仅能获取相对位置信息的场景。
本文引入方向反馈机制于序数回归任务中，即学习者仅获知预测标签相对于真实标签位于左侧或右侧的信息，相较于可获取完整标签的全信息设置，这是一种弱监督形式。我们提出一种基于方向反馈的在线序数回归算法，采用探索-利用策略高效学习。进一步地，设计了核方法变体以在在线环境下学习非线性模型，并通过截断技巧提升内存效率。所提算法在期望意义上保持阈值排序，且达到 $\mathcal{O}(\log T)$ 的期望遗憾。在合成与真实数据集上，与全信息及弱监督算法对比表明，本方法在仅使用方向反馈的情况下表现相当甚至更优。
原文摘要 · Abstract (English)
In this paper, we introduce directional feedback in the ordinal regression setting, in which the learner receives feedback on whether the predicted label is on the left or the right side of the actual label. This is a weak supervision setting for ordinal regression compared to the full information setting, where the learner can access the labels. We propose an online algorithm for ordinal regression using directional feedback. The proposed algorithm uses an exploration-exploitation scheme to learn from directional feedback efficiently. Furthermore, we introduce its kernel-based variant to learn non-linear ordinal regression models in an online setting. We use a truncation trick to make the kernel implementation more memory efficient. The proposed algorithm maintains the ordering of the thresholds in the expected sense. Moreover, it achieves the expected regret of $\mathcal{O}(\log T)$. We compare our approach with a full information and a weakly supervised algorithm for ordinal regression on synthetic and real-world datasets. The proposed approach, which learns using directional feedback, performs comparably (sometimes better) to its full information counterpart.
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