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

TL;DR

This paper introduces accelerated stochastic algorithms for empirical risk minimization that leverage a proximal point framework to improve convergence speed and stability without biasing the original problem.

Contribution

It develops a novel framework based on approximate proximal point methods to accelerate stochastic algorithms for ERM, achieving faster convergence and better stability.

Findings

Improved theoretical convergence rates for ERM algorithms.

Empirical evidence of enhanced stability and efficiency.

Achieves benefits of regularization without bias.

Abstract

We develop a family of accelerated stochastic algorithms that minimize 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. Namely, we provide several algorithms that reduce the minimization of a strongly convex function to approximate minimizations of regularizations of the function. Using these results, we accelerate 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 problem.