On the Convergence of Multicalibration Gradient Boosting

TL;DR

This paper provides theoretical convergence guarantees for multicalibration gradient boosting in regression, showing decay rates of prediction errors and conditions for linear and quadratic convergence, supported by empirical experiments.

Contribution

It offers the first convergence analysis for multicalibration gradient boosting, including decay rates, smoothness-based improvements, and adaptive variant analysis.

Findings

Prediction updates decay at O(1/√T) rate.

Under smoothness, convergence becomes linear.

Experiments confirm theoretical convergence regimes.

Abstract

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.