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In this work we develop a new algorithm for regularized empirical riskminimization. Our method extends recent techniques of Shalev-Shwartz [02/2015],which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes.Moreover, our method is able to better utilize the information in the datadefining the ERM problem. For convex loss functions, our complexity resultsmatch those of QUARTZ, which is a primal-dual method also allowing forarbitrary mini-batching schemes. The advantage of a dual-free analysis comesfrom the fact that it guarantees convergence even for non-convex lossfunctions, as long as the average loss is convex. We illustrate throughexperiments the utility of being able to design arbitrary mini-batchingschemes.

Primal Method for ERM with Flexible Mini-batching Schemes and Non-convex Losses