High-dimensional online calibration from harmonic weights
We study the online calibration of multidimensional forecasts over an arbitrary convex set $Y\subseteq\mathbb{R}^d$ relative to an arbitrary error norm $\|\cdot\|_{L}$. For forecasting $d$ binary outcomes simultaneously ($Y=[0,1]^d$), we give the first algorithm that achieves $\varepsilon$-calibration in a number of rounds that is polynomial in $d$ for every fixed accuracy. It requires $d^{O(1/\varepsilon)}$ rounds, exponentially improving the dimension dependence of previous bounds. For multi-class forecasting ($Y=Δ_d$), we obtain the same $d^{O(1/\varepsilon)}$ rate, improving the $d^{\widetilde{O}(1/\varepsilon^2)}$ bounds of Peng and Fishelson et al. Our algorithm is simple: on each r...
| Authors | Maxwell Fishelson, Mehryar Mohri |
|---|---|
| Primary category | stat.ML |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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