  In this paper we develop an adaptive dual free Stochastic Dual Coordinate
Ascent (adfSDCA) algorithm for regularized empirical risk minimization
problems. This is motivated by the recent work on dual free SDCA of
Shalev-Shwartz (2016). The novelty of our approach is that the coordinates to
update at each iteration are selected non-uniformly from an adaptive
probability distribution, and this extends the previously mentioned work which
only allowed for a uniform selection of "dual" coordinates from a fixed
probability distribution.
  We describe an efficient iterative procedure for generating the non-uniform
samples, where the scheme selects the coordinate with the greatest potential to
decrease the sub-optimality of the current iterate. We also propose a heuristic
variant of adfSDCA that is more aggressive than the standard approach.
Furthermore, in order to utilize multi-core machines we consider a mini-batch
adfSDCA algorithm and develop complexity results that guarantee the algorithm's
convergence. The work is concluded with several numerical experiments to
demonstrate the practical benefits of the proposed approach.
