Before revision:  1) For two-player games, we show that the regret of optimistic Hedge decays at O( 1/T ^{5/6} ), improving the previous bound O(1/T^{3/4}) by \mbox{%DIFAUXCMD syrgkanis2015fast 2) In contrast, we show that the convergence rate of vanilla Hedge is no better than \Omega(1/ T) , addressing an open question posted in \mbox{%DIFAUXCMD syrgkanis2015fast .
After revision:  1) For two-player games, we show that the regret of optimistic Hedge decays at O( 1/T ^{5/6} ), improving the previous bound O(1/T^{3/4}) by Syrgkanis, Agarwal, Luo and Schapire (NIPS'15) 2) In contrast, we show that the convergence rate of vanilla Hedge is no better than \Omega(1/ T) , addressing an open question posted in \mbox{%DIFAUXCMD syrgkanis2015fast .