arXiv subjects

Louis L. Chen

Publications and source records attributed to Louis L. Chen.

3 recordsLinked to original sources

arXiv2026

Perturbation Duality for Robust and Distributionally Robust Optimization: Short and General Proofs

Duality is a foundational tool in robust and distributionally robust optimization (RO/DRO), underpinning both analytical insights and tractable reformulations. Whereas RO/DRO duality is commonly established through minimax arguments or conic duality, we use perturbation duality to obtain new, more general results with short proofs. We show that this perspective provides a natural and unifying framework for deriving RO/DRO dual formulations, proving the associated duality results, and diagnosing the regularity assumptions on which they depend. First, guided by perturbation duality, we establish new duality theorems for a recent DRO framework that unifies several canonical models, including $ϕ$-divergence and Wasserstein models, through optimal transport subject to conditional moment constraints. Our results resolve an open conjecture on this DRO duality by clarifying the role of compactness: compactness itself is not necessary, but can be replaced by perturbation-based regularity conditions. Second, we revisit \emph{robust duality}, commonly described as \emph{primal-worst equals dual-best.} Using bifunctions, we unify dual-best formulations appearing in the literature and derive concise perturbation-based proofs that streamline recent results. Overall, the paper positions perturbation duality as a versatile and underutilized tool for RO and DRO, offering both conceptual unification and technical generality across a broad class of models.

math.OC↗

arXiv2025

Mitigating the Impact of Labeling Errors on Training via Rockafellian Relaxation

Labeling errors in datasets are common, arising in a variety of contexts, such as human labeling, noisy labeling, and weak labeling (i.e., image classification). Although neural networks (NNs) can tolerate modest amounts of these errors, their performance degrades substantially once error levels exceed a certain threshold. We propose a new loss reweighting, architecture-independent methodology, Rockafellian Relaxation Method (RRM) for neural network training. Experiments indicate RRM can enhance neural network methods to achieve robust performance across classification tasks in computer vision and natural language processing (sentiment analysis). We find that RRM can mitigate the effects of dataset contamination stemming from both (heavy) labeling error and/or adversarial perturbation, demonstrating effectiveness across a variety of data domains and machine learning tasks.

cs.LG↗

arXiv2023

Rockafellian Relaxation and Stochastic Optimization under Perturbations

In practice, optimization models are often prone to unavoidable inaccuracies due to dubious assumptions and corrupted data. 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 limit-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. Numerical results in the setting of computer vision and text analytics with label noise illustrate the framework.

math.OC↗