Online Prediction with Limited Selectivity

• URL: http://arxiv.org/abs/2508.09592v1
• Date: Wed, 13 Aug 2025 08:17:12 GMT
• Title: Online Prediction with Limited Selectivity
• Authors: Licheng Liu, Mingda Qiao,
• Abstract summary: Many data statistics can be predicted to a non-trivial error rate without any distributional assumptions or expert advice.<n>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.<n>We study the optimal prediction error both on an instance-by-instance basis and via an average-case analysis.
• Score: 8.540426791244535
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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