Publications

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

Published in arXiv, 2026

Duality is a foundational tool in robust and distributionally robust optimization (RO and DRO), underpinning both analytical insights and tractable reformulations. The prevailing approaches in the literature primarily rely on saddle-point arguments, Lagrangian techniques, and conic duality. In contrast, this paper applies perturbation duality in the sense of Fenchel–Rockafellar convex analysis and demonstrates its effectiveness as a general and unifying methodology for deriving dual formulations in RO and DRO. We first apply perturbation duality to a recently proposed DRO framework that unifies phi-divergence and Wasserstein ambiguity sets through optimal transport with conditional moment constraints. We establish the associated dual representation without imposing compactness assumptions previously conjectured to be necessary, instead introducing alternative conditions motivated by perturbation analysis and leveraging the Interchangeability Principle. We then revisit the concept of robust duality – commonly described as ``primal-worst equals dual-best’’ – and show that perturbation-based formulations provide a unified and transparent characterization of this principle. In particular, we develop a bifunction-based representation that encompasses existing formulations in the literature and yields concise and general proofs, substantially simplifying recent results. This work positions perturbation duality as a versatile and underutilized framework for RO and DRO, offering both conceptual unification and technical generality across a broad class of models.

Recommended citation: Louis Chen, Jake Roth, Johannes Royset (2026). "Perturbation Duality for Robust and Distributionally Robust Optimization: Short and General Proofs" https://arxiv.org/abs/2603.20503

Enhancing Learning with Noisy Labels via Rockafellian Relaxation

Published in The Fourteenth International Conference on Learning Representations (ICLR 2026), 2026

Labeling errors in datasets are common, arising in a variety of contexts, such as human labeling and weak labeling. Although neural networks (NNs) can tolerate modest amounts of these errors, their performance degrades substantially once the label error rate exceeds a certain threshold. We propose the Rockafellian Relaxation Method (RRM)—an architecture-independent, loss reweighting approach to enhance the capacity of neural network methods to accommodate noisy labeled data. More precisely, it functions as a wrapper, modifying any methodology’s training loss, particularly the supervised component. Experiments indicate RRM can provide accuracy improvements across classification tasks in computer vision and natural language processing (sentiment analysis). This potential gain holds irrespective of dataset size, noise generation (synthetic or human), data domain, and adversarial perturbation.

Recommended citation: Louis Chen, Bobbie Chern, Eric Eckstrand, Amogh Mahapatra, Johannes Royset (2026). "Enhancing Learning with Noisy Labels via Rockafellian Relaxation."

On the Adversarial Robustness of Benjamini Hochberg

Published in Thirty-Eighth Annual Conference on Neural Information Processing (NeurIPS 2024), 2024

The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing. Applications of this control abound in drug discovery, forensics, anomaly detection, and, in particular, machine learning, ranging from nonparametric outlier detection to out-of-distribution detection and one-class classification methods. Considering this control could be relied upon in critical safety/security contexts, we investigate its adversarial robustness. More precisely, we study under what conditions BH does and does not exhibit adversarial robustness, we present a class of simple and easily implementable adversarial test-perturbation algorithms, and we perform computational experiments. With our algorithms, we demonstrate that there are conditions under which BH control can be significantly broken with relatively few (even just one) test score perturbation(s), and provide non-asymptotic guarantees on the expected adversarial-adjustment to FDR. Our technical analysis involves a combinatorial reframing of the BH procedure as a balls into bins process, and drawing a connection to generalized ballot problems to facilitate an information-theoretic approach for deriving non-asymptotic lower bounds.

Recommended citation: Louis Chen, Roberto Szechtman, Matan Seri (2024). "On the Adversarial Robustness of Benjamini Hochberg." https://arxiv.org/abs/2501.03402

Rockafellian Relaxation and Stochastic Optimization under Perturbations

Published in Mathematics of Operations Research, 2024

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.

Recommended citation: Johannes Royset, Louis Chen, Eric Eckstrand (2024). "Rockafellian Relaxation and Stochastic Optimization under Perturbations." https://pubsonline.informs.org/doi/full/10.1287/moor.2022.0122

Robustness to Dependency in Influence Maximization

Published in Management Science, 2024

In this paper, we introduce a correlation robust model for the influence maximization problem. Unlike the classic independent cascade model, this model’s diffusion process is adversarially adapted to the choice of seed set. More precisely, rather than only the in- dependent coupling of known individual edge probabilities, we now evaluate a seed set’s expected influence under all possible correlations - specifically, the one that presents the worst-case. We show that any seed set’s worst-case expected influence can be efficiently computed, and though optimizing the worst-case (over seed sets) is NP-hard, a (1 − 1/e) approximation algorithm can be obtained. We provide structural insights from the model and contrast it with the independent cascade model. We discuss how the proposed model can be extended to optimize other objectives by controlling for conservatism using a mix- ture of the independent and the worst-case distribution or by incorporating risk criterion in choosing the seed set. Finally we provide insights from numerical experiments to illustrate the usefulness of the model.

Recommended citation: Louis Chen, Chee Chin Lim, Divya Padmanabhan, Karthik Natarajan (2024). "Robustness to Dependency in Influence Maximization." . https://pubsonline.informs.org/doi/10.1287/mnsc.2021.03445

Distributionally Robust Linear and Discrete Optimization with Marginals

Published in Operations Research, 2021

In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to be specified up to only the marginal distributions. We generalize the primal-dual formulations for this problem from the set of joint distributions with absolutely continuous marginal distributions to arbitrary marginal distributions using techniques from optimal transport theory. While the robust bound is shown to be NP-hard to compute for linear optimization problems, we identify a sufficient condition for polynomial time solvability using extended formulations. This generalizes the known tractability results under marginal information from 0-1 polytopes to a class of integral polytopes and has implications on the solvability of distributionally robust optimization problems in areas such as scheduling which we discuss.

Recommended citation: Louis Chen, Will Ma, Karthik Natarajan, David Simchi-Levi, Zhenzhen Yan. (2021). "Distributionally Robust Linear and Discrete Optimization with Marginals." Operations Research. https://pubsonline.informs.org/doi/10.1287/opre.2021.2243

Correlation Robust Influence Maximization

Published in Thirty-fourth Annual Conference on Neural Information Processing Systems (NeurIPS 2020), 2020

We propose a distributionally robust model for the influence maximization problem. Unlike the classic independent cascade model [16], this model’s diffusion process is adversarially adapted to the choice of seed set. Hence, instead of optimizing under the assumption that all influence relationships in the network are independent, we seek a seed set whose expected influence under the worst correlation, i.e. the “worst-case, expected influence”, is maximized. We show that this worst-case influence can be efficiently computed, and though the optimization is NP-hard, a (1 − 1/e) approximation guarantee holds. We also analyze the structure to the adversary’s choice of diffusion process, and contrast with established models. Beyond the key computational advantages, we also highlight the extent to which the independence assumption may cost optimality, and provide insights from numerical experiments comparing the adversarial and independent cascade model.

Recommended citation: Louis Chen, Divya Padmanabhan, Chee Chin Lim, Karthik Natarajan (2020). " Correlation Robust Influence Maximization." . https://papers.nips.cc/paper/2020/file/4ee78d4122ef8503fe01cdad3e9ea4ee-Paper.pdf

Distributionally Robust Max Flows with Marginals

Published in Symposium on Simplicity in Algorithms (S0SA 2020), 2020

Consider an s-t flow network in which the arc capacities are distributed according to an unknown distribution, but with known marginals. We study the problem of finding a coupling of the marginals that yields the worst, expected Max-flow value. Towards solving this optimization problem, we identify a primal-dual formulation. As one might expect, the form relates to the well-known Max Flow, Min-Cut theorem. And this leads to the rather intriguing interpretation as a 2-player, zero-sum game wherein player 1 chooses what to set the arc capacities to and player 2 chooses an s-t cut. Our contributions in this talk are twofold: (1) we present a linear program (that is efficient with finite-supported marginals) that not only computes the worst-case expected value but is of a form amenable in a two-stage network design formulation, and (2) we show that the problem of finding the worst-case coupling of the stochastic arc capacities boils down to finding an optimal distribution over the set of s-t cuts, which we show can be found efficiently.

Recommended citation: Louis Chen, Will Ma, James Orlin, David Simchi-Levi. (2020). "Distributionally Robust Max Flows with Marginals." SOSA 2020. 1(2). https://www.dropbox.com/s/z59207hnz3iihi0/ltexpprt.pdf?dl=0

On the Structure of Cardinality-Constrained Assortment Optimization

Published in , 2017

We study the static assortment optimization problem with cardinality constraints, i.e., the problem of offering an assortment of items of constrained size that will maximize expected revenue. This is generally regarded as a challenging problem, with identified hardness results in the existing literature for a number of popular and/or well-studied choice models. Motivated by existing approaches in the unconstrained setting that find successful exploitation of identified structure to devise either exact or approximate solution methods, we introduce another structural property of possible interest for study in the cardinality constrained setting. Recently, the work of Jagabathula (2016) has identified the optimality of a local search method for the cardinality constrained static assortment problem under Multinomial Logit (MNL) Choice, making MNL a rare case study of tractability among cardinality constrained problems. So we first revisit the MNL constrained assortment problem under a new lens in search of structure that explains its “tractability.” Following this, we study the extent to which this property holds in other choice models. Indeed, we find that local search is optimal for some other choice models, and remains so even under more generalized cardinality constraints. Finally, we provide and test some algorithms (which require black-box access to the expected revenue function) that can be applied to the joint assortment and pricing problem under certain choice models, showing favorable performance small to moderate-sized problems against some current approaches.

Recommended citation: Louis Chen, David Simchi-Levi. (2017). "On the Structure of Cardinality-Constrained Assortment Optimization." https://www.dropbox.com/s/tbpw3ig9vzrl3xw/AssortmentPaper.pdf?dl=0