AdaBoost's quadratic-over-accuracy convergence conjecture

Let $\bm{\lambda}^*$ be any weight vector and let $B=\|\bm{\lambda}^*\|_1$. For exponential loss $L$ and AdaBoost's iterates, quadratic convergence conjecture. For every $\bm{\lambda}^*$ and every $\varepsilon>0$, AdaBoost reaches loss at most $L(\bm{\lambda}^*)+\varepsilon$ in $O(B^2/\varepsilon)$ rounds, with only absolute constants hidden by the order notation. The paper proves a polynomial rate with a larger exponent and identifies this conjectured monotonicity-based rate as likely but unproved.