On the Convergence of Multicalibration Gradient Boosting
This provides theoretical foundations for a scalable method used in web-scale applications, addressing a gap in understanding its convergence properties.
The paper tackled the lack of convergence guarantees for multicalibration gradient boosting, showing that the multicalibration error decays at O(1/√T) and can improve to linear convergence under smoothness assumptions.
Multicalibration gradient boosting has recently emerged as a scalable method that empirically produces approximately multicalibrated predictors and has been deployed at web scale. Despite this empirical success, its convergence properties are not well understood. In this paper, we bridge the gap by providing convergence guarantees for multicalibration gradient boosting in regression with squared-error loss. We show that the magnitude of successive prediction updates decays at $O(1/\sqrt{T})$, which implies the same convergence rate bound for the multicalibration error over rounds. Under additional smoothness assumptions on the weak learners, this rate improves to linear convergence. We further analyze adaptive variants, showing local quadratic convergence of the training loss, and we study rescaling schemes that preserve convergence. Experiments on real-world datasets support our theory and clarify the regimes in which the method achieves fast convergence and strong multicalibration.