Mitigating the Impact of Labeling Errors on Training via Rockafellian Relaxation

Labeling errors in datasets are common, if not systematic, in practice. They naturally arise in a variety of contexts-human labeling, noisy labeling, and weak labeling (i.e., image classification), for example. This presents a persistent and pervasive stress on machine learning practice. In particular, neural network (NN) architectures can withstand minor amounts of dataset imperfection with traditional countermeasures such as regularization, data augmentation, and batch normalization. However, major dataset imperfections often prove insurmountable. We propose and study the implementation of Rockafellian Relaxation (RR), a new loss reweighting, architecture-independent methodology, for neural network training. Experiments indicate RR can enhance standard neural network methods to achieve robust performance across classification tasks in computer vision and natural language processing (sentiment analysis). We find that RR can mitigate the effects of dataset corruption due to both (heavy) labeling error and/or adversarial perturbation, demonstrating effectiveness across a variety of data domains and machine learning tasks.

Rockafellian Relaxation in Optimization under Uncertainty: Asymptotically Exact Formulations

In practice, optimization models are often prone to unavoidable inaccuracies due to lack of data and dubious assumptions. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on "conservative" decisions. We develop, in contrast, an "optimistic" framework based on Rockafellian relaxations in which optimization is conducted not only over the original decision space but also jointly with a choice of model perturbation. The framework enables us to address challenging problems with ambiguous probability distributions from the areas of two-stage stochastic optimization without relatively complete recourse, probability functions lacking continuity properties, expectation constraints, and outlier analysis. We are also able to circumvent the fundamental difficulty in stochastic optimization that convergence of distributions fails to guarantee convergence of expectations. The framework centers on the novel concepts of exact and asymptotically exact Rockafellians, with interpretations of "negative" regularization emerging in certain settings. We illustrate the role of Phi-divergence, examine rates of convergence under changing distributions, and explore extensions to first-order optimality conditions. The main development is free of assumptions about convexity, smoothness, and even continuity of objective functions.