Skip to yearly menu bar Skip to main content


Poster

Variance-based Regularization with Convex Objectives

Hongseok Namkoong · John Duchi

Pacific Ballroom #212

Keywords: [ Learning Theory ] [ Convex Optimization ] [ Model Selection and Structure Learning ] [ Frequentist Statistics ] [ Regularization ]


Abstract:

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empirical likelihood, and we provide a number of finite-sample and asymptotic results characterizing the theoretical performance of the estimator. In particular, we show that our procedure comes with certificates of optimality, achieving (in some scenarios) faster rates of convergence than empirical risk minimization by virtue of automatically balancing bias and variance. We give corroborating empirical evidence showing that in practice, the estimator indeed trades between variance and absolute performance on a training sample, improving out-of-sample (test) performance over standard empirical risk minimization for a number of classification problems.

Live content is unavailable. Log in and register to view live content