Online Conformal Prediction via Universal Portfolio Algorithms

TL;DR

This paper introduces UP-OCP, a parameter-free online conformal prediction method that leverages universal portfolio algorithms, providing strong finite-time coverage guarantees and improved size/coverage trade-offs over existing methods.

Contribution

The paper develops a general regret-to-coverage theory for online conformal prediction and proposes UP-OCP, a novel, parameter-free algorithm with theoretical guarantees and superior empirical performance.

Findings

UP-OCP achieves better size/coverage trade-offs than prior methods.

Strong finite-time bounds on miscoverage are established.

Extensive experiments demonstrate improved performance across data streams.

Abstract

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-\alpha$ 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 $(1-\alpha)$-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.