提出新方法,在非平稳环境下仍能有效控制预测误差。
Non-Stationary Online Structured Prediction with Surrogate Losses
- 结合动态后悔分析与代理损失优势,设计新型在线学习策略。
- 理论证明误差增长受比较序列总代理损失和路径长度控制。
- 适用于变化环境,对算法设计有指导意义,适合研究者参考。
在线结构化预测任务中,传统基于代理损失的后悔界在非平稳环境中失效,因为固定估计器的代理损失会随时间线性增长。本文提出新上界:累积目标损失不超过 $F_T + O(1 + P_T)$,其中 $F_T$ 为任意比较序列的累积代理损失,$P_T$ 为其路径长度。该界仅通过 $F_T$ 与 $P_T$ 依赖于时间 $T$,因而对非平稳场景更稳健。核心思想是融合在线梯度下降(OGD)的动态后悔分析与‘利用代理差距’技术,揭示了 Polyak 风格学习率的有效性,可导出目标损失界并具有良好实证表现。进一步将方法扩展至卷积 Fenchel–Young 损失框架。最后,构造下界表明对 $F_T$ 与 $P_T$ 的依赖关系是紧的。
原文摘要 · Abstract (English)
Online structured prediction, including online classification as a special case, is the task of sequentially predicting labels from input features. In this setting, the surrogate regret -- the cumulative excess of the actual target loss (e.g., the 0-1 loss) over the surrogate loss (e.g., the logistic loss) incurred by the best fixed estimator -- has gained attention because it admits a finite bound independent of the time horizon $T$. However, such guarantees break down in non-stationary environments, where every fixed estimator may incur surrogate loss that grows linearly with $T$. To address this limitation, we obtain an upper bound of $F_T + O(1 + P_T)$ on the cumulative target loss, where $F_T$ is the cumulative surrogate loss of any comparator sequence and $P_T$ is its path length. This bound depends on $T$ only through $F_T$ and $P_T$, thus offering stronger guarantees under non-stationarity. Our core idea is to combine the dynamic regret analysis of online gradient descent (OGD) with the exploit-the-surrogate-gap technique. This viewpoint sheds light on the usefulness of a Polyak-style learning rate for OGD, which systematically yields target-loss bounds and performs well empirically. We then extend our approach to broader settings beyond prior work via the convolutional Fenchel--Young loss. Finally, a lower bound shows that the dependence on $F_T$ and $P_T$ is tight.
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