Conformal prediction provides a pivotal and flexible technique for uncertainty quantification by constructing prediction sets with a predefined coverage rate. Many online conformal prediction methods have been developed to address data distribution shifts in fully adversarial environments, resulting in overly conservative prediction sets. We propose Conformal Optimistic Prediction (COP), an online conformal prediction algorithm incorporating underlying data pattern into the update rule. Through estimated cumulative distribution function of non-conformity scores, COP produces tighter prediction sets when predictable pattern exists, while retaining valid coverage guarantees even when estimates are inaccurate. We establish a joint bound on coverage and regret, which further confirms the validity of our approach. We also prove that COP achieves distribution-free, finite-sample coverage under arbitrary learning rates and can converge when scores are $i.i.d.$. The experimental results also show that COP can achieve valid coverage and construct shorter prediction intervals than other baselines.

翻译：共形预测通过构建具有预设覆盖率的预测集，为不确定性量化提供了一种关键且灵活的技术。许多在线共形预测方法被开发用于应对完全对抗环境下的数据分布偏移，但这往往导致预测集过于保守。我们提出了乐观共形预测（COP），这是一种将底层数据模式纳入更新规则的在线共形预测算法。通过估计非共形分数的累积分布函数，COP在存在可预测模式时能产生更紧凑的预测集，同时即使在估计不准确时也能保持有效的覆盖率保证。我们建立了关于覆盖率和遗憾值的联合界，进一步证实了所提方法的有效性。我们还证明了COP在任意学习率下均能实现无分布、有限样本的覆盖率，并且在分数为独立同分布时能够收敛。实验结果也表明，COP能够实现有效覆盖，并构建出比其他基线方法更短的预测区间。