Improved and Oracle-Efficient Online $\ell_1$-Multicalibration

We study \emph{online multicalibration}, a framework for ensuring calibrated predictions across multiple groups in adversarial settings, across $T$ rounds. Although online calibration is typically studied in the $\ell_1$ norm, prior approaches to online multicalibration have taken the indirect approach of obtaining rates in other norms (such as $\ell_2$ and $\ell_{\infty}$) and then transferred these guarantees to $\ell_1$ at additional loss. In contrast, we propose a direct method that achieves improved and oracle-efficient rates of $\widetilde{\mathcal{O}}(T^{-1/3})$ and $\widetilde{\mathcal{O}}(T^{-1/4})$ respectively, for online $\ell_1$-multicalibration. Our key insight is a novel reduction of online \(\ell_1\)-multicalibration to an online learning problem with product-based rewards, which we refer to as \emph{online linear-product optimization} ($\mathtt{OLPO}$).

@article{ghuge2025_2505.17365,
  title={ Improved and Oracle-Efficient Online $\ell_1$-Multicalibration },
  author={ Rohan Ghuge and Vidya Muthukumar and Sahil Singla },
  journal={arXiv preprint arXiv:2505.17365},
  year={ 2025 }
}