Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-α$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-α)$-pinball loss. Our first contribution is to identify \emph{linearized regret} as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

翻译：在线保形预测（OCP）旨在为任意（可能对抗性的）数据流构建预测区间，使其在长期运行中达到$1-α$的覆盖水平，同时尽可能保持信息量。现有OCP方法通常需要手动调整学习率才能良好工作，并且可能需要算法特定的分析。本文基于$(1-α)$-分位数损失，为区间值OCP建立了一个通用的遗憾-覆盖理论。我们的第一个贡献是提出**线性化遗憾**作为核心概念，证明控制该遗憾即可为任意在线算法提供覆盖保证。这依赖于一个仅取决于线性化遗憾上界之Fenchel共轭的黑箱归约。基于该理论，我们通过归约到双资产投资组合选择问题，利用通用投资组合算法，提出了UP-OCP——一种无需参数调优的OCP方法。我们证明了UP-OCP即使在预测值多项式增长的情况下，仍具有严格的有限时间误覆盖界。大量实验表明，UP-OCP在区间大小与覆盖率的权衡方面持续优于现有在线保形预测基线方法。