Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization


Roy Frostig, Rong Ge, Sham Kakade, Aaron Sidford ;
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:2540-2548, 2015.


We develop a family of accelerated stochastic algorithms that optimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression, across a wide range of problem settings. To achieve this, we establish a framework, based on the classical proximal point algorithm, useful for accelerating recent fast stochastic algorithms in a black-box fashion. Empirically, we demonstrate that the resulting algorithms exhibit notions of stability that are advantageous in practice. Both in theory and in practice, the provided algorithms reap the computational benefits of adding a large strongly convex regularization term, without incurring a corresponding bias to the original ERM problem.

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