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Exploiting Strong Convexity from Data with Primal-Dual First-Order Algorithms
Jialei Wang · Lin Xiao

Sun Aug 06 10:48 PM -- 11:06 PM (PDT) @ Parkside 2

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems and solved by primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in order to obtain fast linear convergence, and the required dual proximal mapping may not admit closed-form or efficient solution. In this paper, we develop both batch and randomized primal-dual algorithms that can exploit strong convexity from data adaptively and are capable of achieving linear convergence even without regularization. We also present dual-free variants of adaptive primal-dual algorithms that do not need the dual proximal mapping, which are especially suitable for logistic regression.

Author Information

Jialei Wang (University of Chicago)
Lin Xiao (Microsoft Research)

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