带预览的对抗在线分类
Adversarial Online Classification with a Preview
- School of Electrical & Computer Engineering, Tel Aviv University（特拉维夫大学电气与计算机工程学院）
- School of Computer Science, Georgia Institute of Technology（佐治亚理工学院计算机学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出带预览的对抗在线分类模型，刻画了预览率p对二元及多类别分类最优超额损失的影响，提出ChainedPrediction算法以实现精确二元界，用随机预览替代最坏情况序列复杂度。
AI中文摘要：
最坏情况在线分类由序列复杂度（如Littlestone维）决定，即使是VC维为1的阈值这类统计上简单的类别也可能无法实现。我们研究一种预览模型：无知 adversary 固定长度为T的完整标记序列，在预测开始前揭示大小为pT的均匀随机子集，剩余(1-p)T个样本则以原始对抗顺序呈现。针对在未揭示样本上评估的最佳全序列假设，我们刻画了对预览率p的依赖：对于VC维为d的二元类别，最优超额损失为Θ(d/p + √(dT))，上限为T；对于多类别类别，我们得到对应的O~(d_DS/p + √(d_Nat T))界，且不依赖标签数量。因此，随机预览可在不随机化在线顺序的情况下，将最坏情况序列复杂度替换为经典统计维度。为实现该精确二元界，我们的ChainedPrediction算法使用了链式的在线类比，实现为多尺度聚合算法而非仅作为分析论证。
英文摘要：
Worst-case online classification is governed by sequential complexity, such as Littlestone dimension, and can be impossible even for statistically simple classes, such as thresholds of VC dimension one. We study a preview model in which an oblivious adversary fixes an entire labeled sequence of length $T$, a uniformly random subset of size $pT$ is revealed before prediction begins, and the remaining $(1-p)T$ examples are then presented in their original adversarial order. Against the best full-sequence hypothesis evaluated on the unrevealed examples, we characterize the dependence on the preview rate $p$: for binary classes of VC dimension $d$, the optimal excess loss is $Θ(d/p+\sqrt{dT})$, up to the trivial cap at $T$; for multiclass classes we obtain the corresponding $\widetilde O(d_{\rm DS}/p+\sqrt{d_{\rm Nat}T})$ bound with no dependence on the number of labels. Thus a random preview can replace worst-case sequential complexity by classical statistical dimensions without randomizing the online order. To achieve the sharp binary bound, our ChainedPrediction algorithm uses an online analogue of chaining, implemented as a multiscale aggregation algorithm rather than only as an analytic argument.
