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We consider empirical risk minimization of linear predictors with convex lossfunctions. Such problems can be reformulated as convex-concave saddle pointproblems, and thus are well suitable for primal-dual first-order algorithms.However, primal-dual algorithms often require explicit strongly convexregularization in order to obtain fast linear convergence, and the requireddual proximal mapping may not admit closed-form or efficient solution. In thispaper, we develop both batch and randomized primal-dual algorithms that canexploit strong convexity from data adaptively and are capable of achievinglinear convergence even without regularization. We also present dual-freevariants of the adaptive primal-dual algorithms that do not require computingthe dual proximal mapping, which are especially suitable for logisticregression.

Exploiting Strong Convexity from Data with Primal-Dual First-Order Algorithms