Dual Free Adaptive Minibatch SDCA for Empirical Risk Minimization

TL;DR

This paper introduces an adaptive, non-uniform coordinate selection method for dual free SDCA in empirical risk minimization, improving efficiency and convergence, especially on multi-core systems.

Contribution

It extends dual free SDCA by incorporating adaptive, non-uniform coordinate sampling and develops a mini-batch version with proven convergence guarantees.

Findings

Adaptive coordinate selection improves convergence speed.

Mini-batch adfSDCA is effective on multi-core architectures.

Numerical experiments confirm practical benefits.

Abstract

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.