Explicit Asymptotic Bounds for Sequential Calibration Beyond $T^{2/3}$

תקציר מקורי באנגליתarXiv:2610.07623v1 Announce Type: cross Abstract: Probability forecasts are calibrated when predicted probabilities match empirical outcome frequencies: among events assigned a probability $p$, we'd hope that the fraction of positive outcomes is close to $p$. We study the problem of sequential forecasting of binary outcomes. The classical $O(T^{2/3})$ bound on expected cumulative $\ell_1$-calibration error established by Foster and Vohra stood for over two decades until Dagan et al. reduced the exponent $2/3$ by an unspecified constant. We establish a new two-phase recursive labeling strategy for the sign-preservation-with-reuse game that yields the bound $O(n^{\alpha}t^\beta)$ for all choices of space and time. We then sharpen the reduction from upper bounds on sign preservation to calibr