In this paper we develop dual free SDCA with adaptive probabilities for regularized empirical risk minimization. This extends recent work of Shai Shalev-Shwartz [SDCA without Duality, arXiv:1502.06177] to allow non-uniform selection of ”dual” coordinate in SDCA. Moreover, the probability can change over time, making it more efficient than uniform selection. Our work focuses on generating adapti...