Optimization-based Online Conformal Prediction for Multi-step Forecasting

arXiv:2508.13362v2 Announce Type: replace Abstract: Conformal prediction (CP) is well-suited for uncertainty quantification in time series forecasting due to its distribution-free coverage guarantees. However, existing multi-step methods often struggle to balance coverage validity with efficiency: they either calibrate horizons independently, ignoring temporal correlations, or enforce strict simultaneous coverage, resulting in overly conservative intervals. In this work, we propose O2CP: Optimization-based Online Conformal Prediction, a unified framework for online conformal prediction that explicitly models multi-step error dependencies without sacrificing long-term marginal coverage guarantees. We first prove that standard online conformal updates maintain validity as long as calibration parameters remain within a defined "safe" region. Leveraging this theoretical insight, we introduce a two-layer architecture: an outer layer that defines admissible parameter sets to ensure validity, and an inner layer that performs constrained optimization to model joint error distributions and minimize horizon-wide objectives. To make this computationally feasible, we develop a lightweight sampling strategy that estimates joint distributions without requiring large calibration sets. Extensive experiments on real-world datasets, including autonomous driving, climate forecasting, and public health, demonstrate that O2CP consistently outperforms state-of-the-art baselines, achieving target coverage with significantly sharper prediction intervals and reduced regret over long horizons.

Abstract:Conformal prediction (CP) is well-suited for uncertainty quantification in time series forecasting due to its distribution-free coverage guarantees. However, existing multi-step methods often struggle to balance coverage validity with efficiency: they either calibrate horizons independently, ignoring temporal correlations, or enforce strict simultaneous coverage, resulting in overly conservative intervals. In this work, we propose O2CP: Optimization-based Online Conformal Prediction, a unified framework for online conformal prediction that explicitly models multi-step error dependencies without sacrificing long-term marginal coverage guarantees. We first prove that standard online conformal updates maintain validity as long as calibration parameters remain within a defined "safe" region. Leveraging this theoretical insight, we introduce a two-layer architecture: an outer layer that defines admissible parameter sets to ensure validity, and an inner layer that performs constrained optimization to model joint error distributions and minimize horizon-wide objectives. To make this computationally feasible, we develop a lightweight sampling strategy that estimates joint distributions without requiring large calibration sets. Extensive experiments on real-world datasets, including autonomous driving, climate forecasting, and public health, demonstrate that O2CP consistently outperforms state-of-the-art baselines, achieving target coverage with significantly sharper prediction intervals and reduced regret over long horizons.

Machine Learning (cs.LG)

arXiv:2508.13362 [cs.LG]

(or arXiv:2508.13362v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2508.13362 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Optimization-based Online Conformal Prediction for Multi-step Forecasting

Subiecte conexe