High dimensional online calibration in polynomial time
Abstract
In online (sequential) calibration, a forecaster predicts probability distributions over a finite outcome space over a sequence of days, with the goal of being calibrated. While asymptotically calibrated strategies are known to exist, they suffer from the curse of dimensionality: the best known algorithms require days to achieve non-trivial calibration. In this work, we present the first asymptotically calibrated strategy that guarantees non-trivial calibration after a polynomial number of rounds. Specifically, for any desired accuracy , our forecaster becomes -calibrated after days. We complement this result with a lower bound, proving that at least rounds are necessary to achieve -calibration. Our results resolve the open questions posed by [Abernethy-Mannor'11, Hazan-Kakade'12]. Our algorithm is inspired by recent breakthroughs in swap regret minimization [Peng-Rubinstein'24, Dagan et al.'24]. Despite its strong theoretical guarantees, the approach is remarkably simple and intuitive: it randomly selects among a set of sub-forecasters, each of which predicts the empirical outcome frequency over recent time windows.
Cite
@article{arxiv.2504.09096,
title = {High dimensional online calibration in polynomial time},
author = {Binghui Peng},
journal= {arXiv preprint arXiv:2504.09096},
year = {2025}
}