Robust Optimization

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1 paper in the last four weeks, down 75% on the four weeks before. 0.0% of all new papers.

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Latest papers 34

Oct 1, 2026cs.LG

Robust Non-Clairvoyant Scheduling with Classification Models

We study the classical single-machine scheduling problem of minimizing the sum of completion times of jobs in a non-clairvoyant setting, where the processing time of each job remains unknown until its completion. This is a hard problem for which no constant competitive algorithm is possible. Inspired by robust optimization and learning-augmented algorithms, we introduce a novel robustness framework that leverages structural information provided by a classification model to overcome this limitation. Specifically, we assume that jobs are partitioned into classes and we have access to the confusion matrix of the classifier, whose entry

(k,\ell)

indicates the number of jobs predicted to belong to class~

k

but that actually belong to class~

\ell

. In this manner, we are able to characterize uncertainty as a set of permutations within each predicted class, rather than as a collection of discrete numerical scenarios, avoiding the computational difficulty of classical robust metrics, such as Min-Max and Min-Max Regret. In addition to these worst-case metrics, we also consider the expected objective over all scenarios. We first propose an optimal non-adaptive strategy that is oblivious with respect to all three robust criteria. We then investigate adaptive and randomized algorithms, showing that they can outperform the optimal non-adaptive strategy when the matrix exhibits particular structural properties.

Anthony Dugois, Vincent Fagnon, Giorgio Lucarelli

Univ. Marie et Louis Pasteur, CNRS, institut FEMTO-ST, F-25000 Besançon, France · Université de Lorraine, LCOMS, Metz, France

Robust Optimization Learning-Augmented Algorithms

Aug 30, 2026cs.AI

Mitigating Over-Optimization in PRM-Guided Search in Mathematical Reasoning by Optimizing the Guide

Process reward models (PRMs) provide dense step-level guidance for search-based reasoning, enabling inference-time compute to be allocated toward promising partial solutions. However, recent evidence suggests that PRM-guided search can over-optimize imperfect process rewards, pruning viable trajectories while expanding spurious ones. In this work, we theoretically show that directly leveraging PRM score is vulnerable to verifier noise through an extreme-value effect: non-viable prefixes become more likely to receive spuriously high scores as reasoning depth increase. Therefore, we formulate the PRM-guided search as a robust optimization problem over plausible reward perturbations, termed maximin PRM-guided search, leading to a training-free robust process supervision method that preserves promising alternatives when step-level scores are noisy. Maximin PRM-guided search mitigates this failure mode by reducing sensitivity to over-optimized PRM outliers. Without fine-tuning or online adaptation, maximin search consistently improves the PRM-guided search by 17-35% on average, outperforming outcome- and step-level baselines in 14 out of 16 settings. Our source code is available at https://github.com/tjoo512/maximin-search.

Taejong Joo, Diego Klabjan

Department of Industrial Engineering & Management Sciences Northwestern University

Inference-Time Search Process Reward Models Robust Optimization LLM Mathematical Reasoning

Aug 27, 2026cs.LG

Cone Rayleigh Levels: Finite Perturbations and Certified Control

We study the reuse of positive trial profiles under finite perturbations of nonsymmetric matrix pencils B-λG. The lower and upper cone Rayleigh levels need not coincide and are defined without requiring positive eigenvectors. In the positive orthant with positive diagonal

G

, we derive computable perturbation bounds and determine the exact worst-case trial gap over prescribed independent entrywise perturbation classes. This yields the largest uniform radius meeting a given trial-gap tolerance for fixed profiles, certifying trial-value accuracy without recomputation. Experiments on a nonnegative operator and five signed matrices compare sufficient and optimal radii, directional thresholds, and cold- and warm-start recomputation. Several signed cases exhibit severely limited uniform profile reuse despite the optimality of the radius. Exact rational checks verify the reported bounds and worst-case constructions for stored numerical inputs. A finite-budget linear program and differentiable constraints illustrate applications to verified control and learning.

Yavdat Sh. Il'yasov, Nur F. Valeev

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevsky St., Ufa 450008, Russia.

Robust Optimization Spectral Methods

Aug 13, 2026stat.ML

Statistical Properties of Robust Learning under Distributional Shifts

Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and their systematic comparison, remain underexplored: existing analyses typically establish guarantees either in the source environment or for adversarial worst-case performance over an ambiguity set. This paper instead studies generalization error in the target environment---the excess loss under the shifted target distribution. Our contributions are threefold. First, we derive finite-sample generalization error bounds in the shifted target environment for both DRO and RS. These bounds explicitly characterize the trade-off between reduced sensitivity to shift and the regularization penalty induced by each method's robustness hyperparameter, and they avoid the curse of dimensionality associated with Wasserstein empirical concentration. Second, when partial shift information such as shift magnitude or direction is available, we propose information-directed hyperparameter calibrations and compare the two methods given the same information. Under these calibrations, and in the partial-information regimes we study, DRO and RS exhibit complementary theoretical and empirical behavior. Finally, we apply the framework to a network lot-sizing problem, using it to interpret how robust policies respond to positive shifts in the demand distribution. Together, these results fill a gap in understanding the statistical properties of robust learning methods under distributional shifts and provide a principled basis for comparing DRO and RS.

Zhiyi Li, Xiaojie Mao, Yunbei Xu +1

National University of Singapore · Tsinghua University · University College London

Distribution Shift Robustness Distributionally Robust Optimization Robust Optimization Statistical Learning Theory

Aug 10, 2026cs.NE

A Graph Neural Network--Guided Genetic Algorithm for Physical Internet Supply Chain Optimization under Cost Uncertainty

Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared on 15 instances using matched random seeds and fixed limits on distinct assignment evaluations. Because the evaluation budgets for test Instances 13-15 are smaller than the nominal population size, these experiments primarily assess the quality of learned initialization rather than multi-generation evolutionary search. A separate 400-evaluation experiment on exact test Instance 13 permits three complete offspring generations and a partial fourth pass, with GNN-GA outperforming GA in all 10 matched runs. Three independently generated exact-solvable instances provide a separate test of transfer. Ablation results show that learned initialization provides most of the improvement, while entropy-guided mutation has a smaller, instance-dependent effect. Per-instance solution times include GNN inference and search but exclude model training and one-time model setup.

Faezeh Ardali, Gerald M. Knapp

Department of Mechanical and Industrial Engineering Louisiana State University, Baton Rouge, LA, USA

Graph Neural Networks Evolutionary Optimization Combinatorial Optimization Robust Optimization Genetic Algorithms

Aug 5, 2026cs.AI

Posture and Sustainment Optimization Under Adversarial Uncertainty

Pre-commitment posture, the assignment of military assets to theater locations before conflict scenarios resolve, is a critical and formally unsolved problem in joint operational planning. Current practice relies on greedy heuristics that maximize value and ignore geographic coverage and are structurally vulnerable to adversaries that target high-strategic value locations. This paper presents a scenario-weighted adversarially robust posture optimization engine for the Posture and sustainability allocation (PSA) problem, modeled as a finite-horizon Markov Decision Process over assets, theater locations, and time steps. We introduce the Composite Expected Value (CEV) optimizer, which places assets by maximizing scenario-weighted expected posture efficiency over a distribution of threat scenarios, and the RobustCEV extension, which iterates against a Bayesian adversary that updates its targeting distribution in response to observed placement. Across three experiments in an Indo-Pacific basing environment with 20 assets and 5 theater locations, we demonstrate that: (1) the greedy baseline incurs a permanent 25.1% posture efficiency penalty due to geographic under-coverage and a 57.3% scenario-weighted readiness collapse under value-correlated adversarial threat; (2) the CEV optimizer recovers up to 19.8% efficiency over greedy when the threat distribution carries a geographic signal, with a curated set of 5 to 20 scenarios sufficient to capture the majority of this gain; and (3) the RobustCEV extension recovers up to 158% efficiency relative to a naive optimizer when an adaptive adversary employs a deceptive threat prior. All findings are validated using paired t-tests with Bonferroni correction and two-level variance decomposition, confirming that the performance gaps reported are structural properties of placement strategies rather than sampling artifacts.

Amelie Norris, Alyssa Lee, Natan Vidra +1

Robust Optimization Decision-Making under Uncertainty

Jul 30, 2026cs.LG

First-order Constrained Trilevel Optimization Over Distributed Networks for Robust Coreset Selection

With the rapid advancement of the Internet of Things (IoT), massive amounts of data are generated across distributed edge networks. Training models on full data incurs significant computational overhead and storage bottlenecks, rendering coreset selection a critical paradigm. Furthermore, given the privacy-sensitive nature of local data and the escalating demand for model robustness in real-world deployments, developing an effective distributed optimization framework for robust coreset selection is vital, yet remains largely unexplored. To this end, this work first characterizes the hierarchical dependencies among coreset selection, robust optimization, and distributed learning, and formulates the distributed robust coreset selection as a trilevel optimization problem with level-wise constraints. Furthermore, to effectively solve the trilevel problem in a distributed manner, the \underline{F}ederated \underline{F}irst-order \underline{C}onstrained \underline{T}rilevel \underline{O}ptimization (F

^2

CTO) is proposed, which synergistically integrates a hierarchical composite value-function reformulation and a distributed alternating projected gradient algorithm. To the best of our knowledge, F

^2

CTO is the first method developed for distributed robust coreset selection, as well as the first distributed optimization approach for trilevel optimization problems with level-wise constraints. Additionally, we prove that the proposed method achieves a non-asymptotic convergence rate of

\mathcal{O}(ε^{-3/2})

for finding an

ε

-stationary point. Extensive empirical evaluations on reliable continual learning demonstrate the effectiveness and efficiency of the proposed F

^2

CTO.

Yang Jiao, Kaixuan Jiao, Kai Yang +4

Richard · Southeast University · Anhui University +3

Distributed Optimization Robust Optimization Coreset Selection

Jul 29, 2026stat.ML

Expected Survival-Time Bounds for Robust Optimization Over Time under Isotropic Gaussian Dynamics

Robust Optimization Over Time (ROOT) is a recent branch of evolutionary dynamic optimization that seeks solutions capable of remaining effective across multiple consecutive environments. Unlike the traditional track-the-moving-optimum (TMO) paradigm, which reoptimizes after every environmental change, ROOT explicitly values persistence. Although the field has grown considerably, most contributions remain algorithmic and empirical, leaving several fundamental properties poorly understood from a theoretical perspective. One such property is survival time, defined as the number of future environments in which a deployed solution continues to satisfy a prescribed quality threshold. While survival time is widely used as a measure of temporal robustness, little is known about how its expected value depends on environmental dynamics, deployment quality, or problem characteristics. This paper studies expected survival time for a fixed deployed solution under isotropic Gaussian environmental dynamics. Modeling survival as a discrete first-exit problem, we derive a rigorous lower bound and a computable multi-step upper bound. The analysis shows that expected survival scales as

Θ(σ^-{2})

in slowly varying environments and approaches its minimum value of one future change in high dimensions. A comprehensive Monte Carlo study validates the theoretical predictions, examines sensitivity to modeling assumptions and parameter uncertainty, and illustrates how the bounds can support deployment decisions after optimization. The resulting framework provides an analytical characterization of deployment lifetime and identifies when a required deployment horizon can be guaranteed, ruled out, or remains analytically unresolved.

Pavel Novoa-Hernández

Dept. Computer Engineering and Systems Universidad de La Laguna Spain

Robust Optimization

Jul 23, 2026cs.LG

Smart predict-then-robustly-optimize

In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space. While traditional integrated-learning-and-optimization models assume that side information is perfectly revealed, empirical data-driven features are frequently corrupted or noisy at the time of decision-making, leading to fragile operational policies. To bridge this gap, we integrate principles of robust optimization directly into the predictive-prescriptive pipeline via a smart predict-then-robustly optimize loss and establish a computationally tractable convex surrogate, designed to hedge against worst-case feature perturbations. On the theoretical front, we formalize the structural validity of this surrogate by proving its approximation error probability decays exponentially according to a sub-Gaussian concentration profile. Furthermore, we establish that under mild assumptions, the surrogate is Fisher consistent with high probability. We also prove necessary conditions under which our framework outperforms standard smart predict-then-optimize and maintain its superiority even when the standard method is equipped with regularized upstream predictions. Numerical experiments validate that our robust framework consistently yields significant performance improvements over standard methods, both in out-of-sample terms and in training stability.

Aakil Caunhye, Xuefei Lu, Belen Martin-Barragan

Distribution Shift Robustness Predict-Then-Optimize Decision-Focused Learning Robust Optimization Robust Loss Functions Statistical Learning Theory

Jul 15, 2026cs.LG

Maximally Robust Satisficing Bayesian Optimization

Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use. In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.

Samuli Kinnunen, Petrus Mikkola, Antti Niskanen +1

Department of Computer Science, University of Helsinki, Finland · ASM International N.V.

Bayesian Optimization Black-Box Optimization Robust Optimization

Jul 14, 2026cs.IT

Robust Design of Integrated Sensing and Communication in LEO Satellite Systems

With the growing demand for satellite sensing and communication, the limited wireless resources are difficult to support multiple satellite systems. Therefore, it is desired to investigate integrated sensing and communication (ISAC) in low Earth orbit (LEO) satellite systems to enable multi-functionality within a single satellite, thereby saving both spectrum and orbital resources. In this paper, a framework for ISAC in LEO satellite systems is established, where a satellite can simultaneously sense multiple targets and serve multiple communication users (CUs) over the same spectrum. Considering the limited onboard energy of satellite, a novel robust beamforming design algorithm is developed with the goal of minimizing total transmit power while satisfying the mean squared error (MSE) requirements for sensing and signal-to-interference-plus-noise ratio (SINR) requirements for communication in presence of channel phase uncertainty which exacerbates the cross-functional interference. According to theoretical analysis, the proposed algorithm for ISAC in LEO satellite systems is effective. Moreover, extensive simulations confirm the superiority of the proposed algorithm over baselines.

Hezhen Yang, Xiaoming Chen, Qi Wang

College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China

Integrated Sensing and Communication Robust Optimization Wireless Communications LEO Satellite Networks Wireless Resource Allocation

Jul 6, 2026cs.RO

SLAM: Structured and Localized Analytic Manifold Adaptation for Lifelong VPR

Visual Place Recognition (VPR) in lifelong deployment requires continuous adaptation to new environments without catastrophic forgetting. In this paper, we propose SLAM, a Structured and Localized Analytic Manifold adaptation framework. Our framework elegantly unifies uncertainty-aware smoothing via Unscented transformation, topological space partitioning through a Gaussian Mixture Model (GMM), and

H_\infty

robust bound optimization into a singular, unified closed-form analytical recursion. Exhaustive ablation studies demonstrate that while the synergistic combination of uncertainty smoothing and localized mapping (U+G configuration) achieves the state-of-the-art nominal accuracy of 27.5%, the full deployment of the

H_\infty

bound does not require an architectural split; rather, it introduces a mathematically guaranteed minimax robust bound. This formulation enables the system to seamlessly modulate the intrinsic trade-off between nominal placement precision and worst-case disturbance attenuation through a single regularization parameter.

Kenta Tsukahara, Kanji Tanaka, Rai Hisada

Department of Mechanical Engineering, Faculty of Engineering, University of Fukui, Fukui 910-8507, Japan

Visual Place Recognition Continual Learning Robust Optimization

Jul 2, 2026cs.AI

Distributionally Robust Listwise Preference Optimization

Existing robust preference optimization for language-model alignment mainly studies pairwise supervision and places robustness at the dataset, prompt, or preference-pair level. We instead study listwise preference optimization under ranking-label uncertainty: given a prompt and a candidate list, the observed ranking over that list may be ambiguous due to annotator inconsistency, near-ties, lossy rankwise feedback, or reward-model noise. We propose a pointwise total-variation robust Plackett--Luce objective that directly robustifies the ranking label conditional on the candidate list. The robust loss admits an exact decomposition into the nominal PL loss plus a worst-case PL correction, and the worst-case ranking is obtained by sorting current implicit scores in ascending order, reducing the inner maximization from

K!

enumeration to

O(K\log K)

. This tractable structure yields strong offline and online optimization guarantees. In the offline fixed-list setting, the robust objective is convex and projected stochastic subgradient reaches global

ε

-suboptimality with

O(ε^{-2})

sample complexity. In the online policy-induced setting, where candidate lists are generated by the current policy, we establish weak convexity and

\widetilde O(ε^{-2})

Moreau-envelope stationarity. Experiments in offline LLM alignment show that the proposed robust correction largely preserves performance under clean labels and improves robustness under noise. In online alignment, it makes reward-model-ranked candidate expansion more reliable and improves both reward-model and external GPT-4 judge metrics.

Xudong Wu, Jian Qian, Pangpang Liu +2

The University of Hong Kong · Hong Kong SAR · Yale University +3

LLM Alignment Distributionally Robust Optimization Robust Optimization Robust Loss Functions Preference Optimization

Jun 30, 2026cs.AI

RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search

Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods optimize heuristics for a fixed training instance set and may fail catastrophically when deployed under real-world distributional shifts. We propose Robust Adversary Instance Search (RAISE), a framework that integrates constrained worst-case instance search within a principled neighborhood of the training distribution into the LLM-based evolutionary search loop. RAISE treats robust AHD as a constrained adversarial instance search problem: the outer loop evolves heuristics via LLM operators, while an LLM-free inner loop efficiently identifies hard instances within an epsilon-ball around the training instance set using a basis distribution parameterization with boundary projection. Comprehensive experiments on Online Bin Packing (OBP), Online Job Shop Scheduling (OJSP), and Online Vehicle Routing (OVRP) across five distribution families demonstrate that existing LLM-based AHD methods degrade by up to 19 times under distribution shift, while RAISE consistently maintains strong performance across all tested distributions and problem scales

Fei Liu, Alessio Figalli, Patrick Owen +1

University of Zurich · 2ETH Zurich

Distribution Shift Robustness Automated Algorithm Discovery Automated Heuristic Design Large Language Model-Guided Optimization Robust Optimization

Jun 29, 2026cs.LG

Robust Strategic Classification under Decision-Dependent Cost Uncertainty

Humans facing algorithmic decision systems have been found to ``game'' them by altering their input data (at a cost to them) in order to favorably change the algorithmic outcomes they receive (at a cost to the algorithm). The growing literature on strategic classification seeks to develop robust machine learning algorithms that account for, and reduce, unwanted strategic behavior. A limitation of these existing works is that they assume the cost of strategic behavior to be fixed and independent of the classifier's decision. In practice, however, manipulation costs evolve and depend on past algorithmic decisions: today's decisions influence tomorrow's costs. This paper proposes and analyzes a two-stage robust optimization framework with a decision-dependent uncertainty set to capture such dependencies. We highlight that awareness of policy-dependent costs not only reduces uncertainty, but also better curtails gaming of the algorithmic system over time.

Sura Alhanouti, Güzin Bayraksan, Parinaz Naghizadeh

Department of Integrated Systems Engineering, The Ohio State University, Ohio, USA · Department of Industrial Engineering, Jordan University of Science and Technology, Irbid, Jordan · Department of Electrical and Computer Engineering, University of California, San Diego, USA

Strategic Classification Robust Optimization Decision-Making under Uncertainty

Jun 22, 2026cs.AI

YUKTI: From Natural-Language Situations to Robust, Verifiable Decisions An Uncertainty-Typed Proposition IR, Assumption-Robust Pareto Frontiers, and a Regret Certificate

Language models turn a worded situation into a numeric plan, and the dominant pipelines (NL4Opt, OptiMUS, ORLM, OR-LLM-Agent) commit to a single objective and point-valued coefficients, then solve once. For decisions that allocate real budget, effort, or clinical attention, that confidence is the failure mode: every objectified number is an assumption, and a plan optimal only if the guesses are exactly right is fragile -- mimicry of computation. YUKTI changes the target of autoformulation. Its representation is a typed-proposition graph whose relationships carry shape priors, coefficient uncertainty, and provenance. YUKTI routes each stage to an exact, nonlinear, or evolutionary solver; couples stages by a distributional Pareto hand-off; and introduces Assumption-Robust Pareto Frontiers (ARPF), resampling assumptions (including structural epsilon-contamination) to score how often each action survives (rho). We prove a bound making rho an exact factor of decision regret, add auditable traceability, and synthesize a benchmark-faithful data foundation when none exists (SRJANA). We validate three ways: under controlled misspecification the robust compromise cuts mean and tail regret by over 90% versus a naive point plan; on a regulated commercial decision we optimize inside a lawful action space and price the downside in euros; and on a real public dataset of 41,188 decisions an out-of-sample backtest beats the logged status quo by 34% and a naive point rule by 4% while reducing the optimizer's curse. The solvers are standard; we claim no benchmark-SOTA win. A head-to-head shows an LLM given the correct numbers, and single-objective optimization, both incur about 47x the held-out regret of YUKTI -- an LLM is a formulator, not a solver. Under long-range causal coupling, the forward hand-off becomes unsound, locating where it must become a backward-induction causal policy.

Suyash Mishra

AI Researcher

Large Language Model-Guided Optimization Robust Optimization Regret Minimization Uncertainty Propagation Multi-Objective Optimization Natural Language to Optimization Modeling+1

Jun 21, 2026cs.LG

Generative Robust Optimisation

Classical uncertainty sets for robust optimisation impose fixed geometric shapes that cannot represent the complex dependencies present in real-world data. We propose Generative Robust Optimisation (GRO), a framework in which a deep generative model defines the uncertainty set as the image of a neural network decoder over a calibrated latent set, naturally accommodating nonlinear correlations, asymmetry, and multimodality. A five-point evaluation framework (reconstruction fidelity, distribution matching, latent regularity, robust relevance, and computational tractability) provides systematic, model-agnostic criteria for assessing any neural network-based uncertainty set. We instantiate this framework with a Wasserstein Adversarial Autoencoder employing Gaussian mixture model-guided training for latent regularity and constraint-consistency regularisation for robust relevance. Restricting the decoder to ReLU activations enables exact worst-case verification through mixed-integer programming embedding. Extensive experiments on a production planning problem across six uncertainty distributions and six generative architectures, together with a multi-period facility location study, validate the framework and demonstrate that systematic attention to all five criteria yields uncertainty sets that are simultaneously expressive, well-calibrated, and optimisation-tractable.

Yuhui Yin, Vassilis M. Charitopoulos

Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, UCL (University College London), Torrington Place, London WC1E 7JE, UK

Robust Optimization Mixed-Integer QP

Jun 12, 2026cs.LG

Which Directions Matter? Sparse Design for Affine Robust Optimization

Robust machine learning and optimization rely on the uncertainty model choice. We investigate which uncertainty directions a model must cover when defined by a finite dictionary and a budget constraint. Selecting a subset forms an atomic uncertainty set with a closed form support function, yielding tractable robust programs for affine objectives. We propose a data driven selection rule based on a coverage objective over evaluation directions, including gradients, adversarial perturbations, or shifts observed on held out data. We prove this objective is monotone and submodular, supporting a greedy method with a

(1-1/e)

approximation guarantee and a matching hardness barrier. We also provide a certificate bounding the loss from the selected subset and a radius calibration rule with out of sample control.

Pedro Chumpitaz-Flores, My Duong, Juan S. Borrero +1

University of South Florida, Tampa, FL, USA

Robust Optimization Decision-Making under Uncertainty

Jun 2, 2026stat.ML

A Robust Optimization Approach to Sparse Principal Component Analysis

While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data. Existing methods address this by promoting sparsity through explicit

\ell_1

-penalties, but these are not obvious to tune due to the unsupervised nature of the task. In contrast, we propose Adversarial PCA (AdvPCA), which leverages robust optimization to achieve sparsity by optimizing the reconstruction objective against bounded, worst-case latent space perturbations. We show that this formulation admits a closed-form reduction, leading to a practical iterative algorithm that alternates between adversarial linear regression-style updates for the sparse encoder and orthogonal updates for the decoder. By theoretically characterizing the solution, we derive a data-adaptive parameterization that allows the algorithm to perform effectively out of the box. We validate these claims through numerical experiments on synthetic and real-world genomics data.

David Vävinggren, Francis Bach, André M. H. Teixeira +2

Uppsala University, Sweden · PSL Research University / INRIA, France · Science for Life Laboratory, Sweden

Principal Component Analysis Robust Optimization Dimensionality Reduction

May 27, 2026cs.LG

Unification and Optimization of Robust Supervised Learning

The literature has proposed various robust alternatives to empirical risk minimisation to address failure modes such as distribution shift, label noise and finite-sample degeneracies. Examples include distributionally robust optimization, label smoothing, vicinal risk minimization, and Mixup. However, such approaches are typically developed in isolation, forcing practitioners to commit a priori to a single failure mode even when the dominant mode for the task is unclear. To address this, we organize a broad class of existing methods along three common design axes and derive a tractable training procedure that decomposes robust learning into sequential stages (reference distribution enrichment, input-space perturbation, label-space perturbation, and sample-level aggregation), each with a choice of stance (pessimistic, neutral, or optimistic). This results in a unified design space in which joint hyperparameter optimization can compose and configure robustness strategies suited to the task at hand. Across tabular, image, and reward modeling benchmarks, joint hyperparameter optimization is competitive with the best single-method baseline in each setting, offering a reliable default for practitioners who do not know a priori which failure mode dominates their task.

Jonas Hanselle, Valentin Margraf, Clemens Damke +1

LMU Munich, MCML · LMU Munich, MCML, DFKI

Distribution Shift Robustness Robust Optimization Learning with Noisy Labels

May 20, 2026eess.SY

Secure Coordination for Vertiport Sequencing in Advanced Air Mobility

Advanced air mobility operations will require reliable coordination mechanisms for managing dense traffic near vertiports. However, sequencing decisions may become vulnerable when they rely on potentially falsified self-reported information such as estimated time of arrival. Self-interested vehicles may misreport their arrival times to obtain favorable landing priority, while malicious actors may spoof information to disrupt sequencing decisions or induce unnecessary congestion. This paper studies secure coordination for vertiport sequencing under sensing uncertainty. We consider a coordinator that combines self-reported Remote-ID information with externally obtained surveillance measurements to check reports and assign separation-feasible arrival schedules. Since surveillance-based estimates are uncertain, falsified reports may remain consistent with the sensing uncertainty region and cannot always be rejected outright. We therefore formulate sequencing as a robust design problem over this uncertainty region. Self-interested misreporting is modeled as a strategic deviation that improves the reporting vehicle's own sequencing outcome, whereas malicious spoofing is modeled as an adversarial disturbance that degrades the system-level objective. The final paper will develop robust sequencing rules over surveillance-consistent uncertainty sets and evaluate their performance in representative vertiport sequencing scenarios.

Jaehan Im, Filippos Fotiadis, Ufuk Topcu +1

Graduate Research Assistant, Department of Aerospace Engineering and Engineering Mechanics · Postdoctoral Researcher, Oden Institute for Computational Engineering & Sciences · Professor, Oden Institute for Computational Engineering & Sciences +1

Multi-Agent Coordination False Data Injection Attacks Robust Optimization

May 14, 2026cs.AI

Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty

Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable computation. However, existing methods are largely problem-agnostic, operating solely on the uncertainty set without consulting the feasible region or recourse structure. In this paper, we introduce PRISE, a problem-driven sequential lookahead heuristic that constructs reduced scenario sets by evaluating the marginal impact of each scenario. While PRISE yields high-quality scenario subsets, each selection step requires solving multiple subproblems, making it computationally expensive at scale. To address this, we propose NeurPRISE, a neural surrogate model built on a GNN-Transformer backbone that encodes the per-scenario structure via graph convolution and captures cross-scenario interactions through attention. NeurPRISE is trained via imitation learning with a gain-aware ranking objective, which distills marginal gain information from PRISE into a learned scoring function for scenario ranking and selection. Extensive results on three 2RO problems show that NeurPRISE consistently achieves competitive regret relative to comprehensive methods, maintains strong calability with varying numbers of scenarios, and delivers 7-200x speedup over PRISE. NeurPRISE also exhibits strong zero-shot generalization, effectively handling instances with larger problem scales (up to 5x), more scenarios (up to 4x), and distribution shifts.

Tianjue Lin, Jianan Zhou, Jieyi Bi +4

Nanyang Technological University · Eindhoven University of Technology · Shandong University +1

Neural Surrogate Modeling Robust Optimization

May 12, 2026cs.AI

Automated Reformulation of Robust Optimization via Memory-Augmented Large Language Models

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its practical use is often limited by the need to manually reformulate uncertain optimization models into tractable deterministic counterparts. Recent large language models (LLMs) have been shown promising for automating optimization formulation, yet RO reformulation remains challenging because it requires precise multi-step reasoning and mathematically consistent transformations. To facilitate systematic evaluation of LLM-based reformulation, for which no dedicated benchmark currently exists, we develop AutoRO-Bench, a benchmark featuring an automated data generation pipeline for the core RO reformulation task and a curated dataset for the RO application task. To address the reformulation challenge, we propose Automated Reformulation with Experience Memory (AutoREM), a tuning-free memory-augmented framework that autonomously builds a structured textual experience memory by reflecting on past failed trajectories through a tailored offline adaptation procedure. AutoREM requires neither domain-specific expert knowledge nor parameter updates, and the resulting memory readily transfers across different base LLMs. Experimental results show that AutoREM consistently improves the accuracy and efficiency of RO reformulation across in-distribution datasets, out-of-distribution datasets, and diverse base LLMs.

Jinbiao Chen, Shuang Jin, Guoyun Zhang +3

Department of Industrial Systems Engineering and Management, National University of Singapore · Department of Data and Systems Engineering, The University of Hong Kong · Institute of Operations Research and Analytics, National University of Singapore +1

Memory-Augmented Language Models Large Language Model-Guided Optimization Robust Optimization

May 10, 2026cs.CV

Outlier-Robust Diffusion Solvers for Inverse Problems

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

Yang Zheng, Jiahua Liu, Tongyao Pang +2

School of Computer Science and Engineering, University of Electronic Science and Technology of China · Yau Mathematical Sciences Center, Tsinghua University

Diffusion Models for Image Restoration Robust Optimization Diffusion-Based Inverse Problems Inverse Problems Image Inverse Problems

May 8, 2026cs.LG

Learning Polyhedral Conformal Sets for Robust Optimization

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.

Shuyi Chen, Wenbin Zhou, Shixiang Zhu

Carnegie Mellon University

Conformal Prediction Robust Optimization Decision-Making under Uncertainty

May 7, 2026cs.LG

Distributionally-Robust Learning to Optimize

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance estimation problem (PEP) over algorithm parameters such as step sizes. Our framework unifies two extremes: as the robustness radius vanishes, we recover classical learning to optimize (L2O); as it grows, we recover worst-case optimal algorithm design via PEP. We solve the resulting problem with stochastic gradient descent, differentiating through the solution of an inner semidefinite program at each step. We prove high-probability bounds showing that the true risk of the learned algorithm is at most the in-sample L2O optimum plus a slack that shrinks with the sample size, and is no worse than the worst-case PEP bound. On unconstrained quadratic minimization, LASSO, and linear programming benchmarks, our learned algorithms achieve strong out-of-sample performance with certifiable robustness, outperforming both worst-case optimal and vanilla L2O baselines.

Vinit Ranjan, Jisun Park, Bartolomeo Stellato

Department of Operations Research and Financial Engineering, Princeton University. · Department of Operations Research and Financial Engineering, Princeton University, and Research Institute of Mathematics, Seoul National University. · Research Institute of Mathematics, Seoul National University.

Learning to Optimize Distributionally Robust Optimization Robust Optimization Wasserstein Distributionally Robust Optimization

May 7, 2026cs.LG

From Dual Tracking to Clipping: Provably Faster Distributionally Robust Multi-Objective Optimization

Multi-objective optimization (MOO) has received growing attention in applications that require learning under multiple criteria. However, most existing MOO formulations do not explicitly account for distributional shifts in the data. We introduce distributionally robust multi-objective optimization (DR-MOO), which minimizes multiple objectives under their respective worst-case distributions. We propose Pareto-type solution concepts for DR-MOO and develop multi-gradient descent algorithms (MGDA) with provable guarantees. Leveraging a Lagrangian dual reformulation, we first design a double-loop MGDA that uses an inner loop to estimate dual variables and achieves a total sample complexity

\mathcal{O}(ε^{-8})

for reaching an

ε

-Pareto-stationary point. To further improve convergence, we combine large-batch sampling with gradient clipping to accommodate generalized smoothness and control bias in stochastic preference updates, eliminating the need for double sampling. This yields a single-loop double-clip MGDA with substantially improved sample complexity

\mathcal{O}(ε^{-4})

. Our theory applies to nonconvex problems without requiring uniformly bounded gradients of the dual objectives. Experiments demonstrate that our methods are competitive with state-of-the-art MGDA baselines.

Yufeng Yang, Fangning Zhuo, Ziyi Chen +2

Texas A&M University · A*STAR · University of Maryland

Gradient Clipping Gradient Descent Nonconvex Stochastic Optimization Distributionally Robust Optimization Robust Optimization Multi-Objective Optimization

Apr 30, 2026math.OC

Sampler-Robust Optimization under Generative Models

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

Ziwei Zhang, Jonathan Yu-Meng Li

Telfer School of Management University of Ottawa

Distribution Shift Robustness Distributionally Robust Optimization Robust Optimization

Jan 16, 2026stat.ML

Contextual Distributionally Robust Optimization with Causal and Continuous Structure

We propose a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution, and we develop an interpretable and tractable decision rule. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving causal consistency. We then formulate a contextual DRO model with a CSD-based ambiguity set, termed Causal Sinkhorn DRO (Causal-SDRO), and derive its strong dual reformulation, where the worst-case distribution is characterized as a mixture of Gibbs distributions. To obtain an (infinite-dimensional) optimal policy, we propose a soft regression forest (SRF) decision rule: it preserves the interpretability of classical decision trees while being fully parametric, differentiable, and Lipschitz-smooth, enabling intrinsic interpretation from both global and local perspectives. To solve the Causal-SDRO with parametric decision rules, we develop an efficient stochastic compositional gradient algorithm that converges to an

\varepsilon

-stationary point at a rate of

\mathcal{O}(\varepsilon^{-4})

, matching that of standard stochastic gradient descent. Finally, we validate our method through numerical experiments on synthetic and real-world datasets, demonstrating its superior performance and interpretability.

Fenglin Zhang, Jie Wang

School of Artificial Intelligence The Chinese University of Hong Kong, Shenzhen Shenzhen, 518172, China · School of Artificial Intelligence, School of Data Science The Chinese University of Hong Kong, Shenzhen Shenzhen, 518172, China

Stochastic Optimization Distributionally Robust Optimization Robust Optimization Wasserstein Distributionally Robust Optimization Optimal Transport

Apr 15, 2025math.OC

Wasserstein Distributionally Robust Regret Optimization

Distributionally robust optimization (DRO) is widely used for decision-making under uncertainty, but its adversarial focus on worst-case loss can lead to overly conservative policies. To mitigate this, we study ex-ante Distributionally Robust Regret Optimization (DRRO) with Wasserstein ambiguity sets, designed to balance robustness with upside potential. We develop a theory of Wasserstein DRRO (WDRRO) paralleling Wasserstein DRO. Under smoothness and regularity, WDRRO selects among ERM optima by a first-order gradient-discrepancy rule. If the ERM optimizer is unique, first-order sensitivity vanishes and a second-order expansion governs deviations. For convex quadratics ERM and DRRO coincide for any radius. We then study regimes where these assumptions fail: nondifferentiable max-affine losses, discrete references, and larger radii, where WDRRO can differ from ERM and WDRO. We show that computing WDRRO regret is NP-hard even without bilinear terms. Nevertheless, we develop exact algorithms, a tractable convex relaxation with guarantees, and experiments showing tightness and loss-dependent behavior.

Lukas-Benedikt Fiechtner, Jose Blanchet

Institute of Computational and Mathematical Engineering Stanford University · Institute of Computational and Mathematical Engineering Department of Management Science and Engineering Stanford University

Distributionally Robust Optimization Robust Optimization Wasserstein Distributionally Robust Optimization