无需调参的在线预测区间方法，覆盖准确且区间更紧凑。
Online Conformal Prediction via Universal Portfolio Algorithms
- 用线性化损失控制覆盖率，构建通用理论框架。
- 提出UP-OCP，实现有限时间内的低误覆盖率，支持多项式增长预测。
- 适合对预测可靠性要求高的实时数据场景，如金融、工业监控。
在线共形预测（OCP）旨在为任意（可能对抗性）数据流生成具有长期 $1-α$ 覆盖率的预测区间，同时尽可能提高信息量。现有方法常需手动调整学习率，且依赖特定算法分析。本文基于 $(1-α)$-pinball 损失，建立通用的“后悔值到覆盖率”理论。首次提出“线性化后悔”作为核心概念，证明其控制可导出任意在线算法的覆盖率边界。该理论通过仅依赖线性化后悔上界Fenchel共轭的黑箱归约实现。在此基础上，提出UP-OCP：一种参数无关的OCP方法，通过归约至双资产投资组合选择问题，利用通用投资组合算法。理论证明了在多项式增长预测下仍具备强有限时间误覆盖边界。大量实验表明，UP-OCP在大小与覆盖率权衡上优于已有基线方法。
原文摘要 · Abstract (English)
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.
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