AdaBoost's near-optimal convergence conjecture for ternary feature matrices

Let $m$ be the number of training examples and suppose the feature matrix has entries in $\{-1,0,+1\}$. Let $L$ denote the exponential loss and let $\inf_{\bm{\lambda}}L(\bm{\lambda})$ be its optimal value. Near-optimal convergence conjecture. For every $\varepsilon>0$, AdaBoost reaches loss at most $\inf_{\bm{\lambda}}L(\bm{\lambda})+\varepsilon$ within

$$2^{O(m\ln m)}\varepsilon^{-(1+o(1))}$$

rounds. Existing bounds in the paper have comparable dependence on $m$ but worse dependence on $\varepsilon$; this conjecture would give a nearly optimal rate.