Online Prediction with Limited Selectivity
Abstract
Selective prediction [Dru13, QV19] models the scenario where a forecaster freely decides on the prediction window that their forecast spans. Many data statistics can be predicted to a non-trivial error rate without any distributional assumptions or expert advice, yet these results rely on that the forecaster may predict at any time. We introduce a model of Prediction with Limited Selectivity (PLS) where the forecaster can start the prediction only on a subset of the time horizon. We study the optimal prediction error both on an instance-by-instance basis and via an average-case analysis. We introduce a complexity measure that gives instance-dependent bounds on the optimal error. For a randomly-generated PLS instance, these bounds match with high probability.
Cite
@article{arxiv.2508.09592,
title = {Online Prediction with Limited Selectivity},
author = {Licheng Liu and Mingda Qiao},
journal= {arXiv preprint arXiv:2508.09592},
year = {2025}
}