Before revision:  Our results apply to both the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, as well as those more general divergence measures which allow heavy tail ones such as student t and lognormal distributions .
After revision:  Our results apply to both the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, our results apply to divergence measures that accommodate well heavy tail distribution such as the student t-distribution and the lognormal distribution. Comprehensive testings on synthetic data and real data are provided .