Variance-based regularization with convex objectives

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.

Cited by in corpus (8)

• Training individually fair ML models with Sensitive Subspace Robustness
• Device Heterogeneity in Federated Learning: A Superquantile Approach
• Federated Learning with Superquantile Aggregation for Heterogeneous Data
• Stability and Generalization of Stochastic Gradient Methods for Minimax Problems
• Learning with risks based on M-location
• A Survey of Learning Criteria Going Beyond the Usual Risk
• Robust Sampling in Deep Learning
• DROMO: Distributionally Robust Offline Model-based Policy Optimization