无悔学习与在线保形预测的关系
The Relationship between No-Regret Learning and Online Conformal Prediction
- University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文探究无悔学习与在线保形预测的关系，发现标准无悔保证在对抗环境或组条件覆盖场景下失效，证明阈值校准覆盖与交换无悔的紧密联系，且跟随扰动领导者家族算法可提供组条件覆盖保证，还分析实验了ACI算法的多组泛化版本。
AI中文摘要：
现有在线保形预测算法——可在对抗性环境中保证边际覆盖——是在线梯度下降（OGD）的变体，但其最坏情况覆盖的分析并非源于OGD的无悔保证。无悔学习与在线保形预测有何关系？我们观察到，尽管标准无悔保证在独立同分布（i.i.d.）环境中可推导出边际覆盖，但一旦转向对抗性环境或要求组条件覆盖，这种关联便会失效。另一方面，我们证明了对抗性环境中阈值校准覆盖与交换无悔之间存在紧密联系，且该联系可扩展至组条件（多有效）覆盖。我们还表明，无悔学习算法中的跟随扰动领导者（包括OGD）家族算法，可用于在对抗性环境中为任意分组函数提供组条件覆盖保证。通过这一联系，我们分析并实验了Gibbs & Candes [2021]（arXiv:2106.00170）的ACI算法的多组泛化版本。
英文摘要：
Existing algorithms for online conformal prediction -- guaranteeing marginal coverage in adversarial settings -- are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between threshold calibrated coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the follow the perturbed leader family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs & Candes [2021] (arXiv:2106.00170).
