We consider the question of learning the natural parameters of a $k$ parameter \textit{minimal} exponential family from i.i.d.

We consider the question of learning the natural parameters of a k parameter \textit{minimal} exponential family from i.i.d. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We provide finite sample guarantees to achieve an ( \ell_2) error of \alpha in the parameter estimation with sample complexity O(\mathrm{poly}(k/\alpha)) and computational complexity {O}(\mathrm{poly}(k/\alpha)) .