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Distributionally Robust Optimization: A Review
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Distributionally Robust Optimization: A Review
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The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.
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Cited by 32 Pith papers
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Taming the Curses of Multiagency in Robust Markov Games with Large State Space through Linear Function Approximation
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Navigating the Safety-Fidelity Trade-off: Massive-Variate Time Series Forecasting for Power Systems via Probabilistic Scenarios
Introduces PowerPhase benchmark for massive-variate power-system forecasting and PowerForge model that achieves best average rank on safety-fidelity metrics across all tested grids.
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Conformal Risk Sharing: Certified Cost Allocation with Participation Guarantees
Conformal Risk Sharing combines an interpretable sharing policy tuned on training data with split conformal calibration on held-out data to produce certified obligation caps and bounded aggregate harm without distribu...
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Conformal Risk-Averse Decision Making with Action Conditional Guarantee
Action-conditional conformal prediction sets provide per-action safety guarantees for risk-averse policies that optimize conditional value-at-risk through pinball-loss minimization.
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Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
A distributionally robust safety filter reduces certification for nonlinear systems under arbitrary uncertainties to a one-dimensional switching-time search with Wasserstein-inflated sampling guarantees.
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Integrating Feature Correlation in Differential Privacy with Applications in DP-ERM
CorrDP relaxes standard differential privacy by incorporating feature correlations, enabling distance-dependent noise in DP-ERM for better privacy-utility tradeoffs.
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Near-Optimal Policy Identification in Robust Constrained Markov Decision Processes via Epigraph Form
Presents the first algorithm to identify an ε-optimal policy in robust constrained MDPs via epigraph form and bisection search with Õ(ε^{-4}) robust policy evaluations.
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Minimizing Upper Confidence Bounds: A Data-Driven Framework for Stochastic Programming
Proposes APUB optimization framework for stochastic programming, proves asymptotic correctness and consistency of the new bound, and develops bootstrap and L-shaped solvers for two-stage linear problems with empirical...
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Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback
Wasserstein distributionally robust regret optimization for RLHF admits a promptwise water-filling solution and a GRPO-compatible sampled bonus that mitigates over-optimization better than value-robust DRO.
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Trustworthy Recommendation in the Era of Large Language Models: Opportunities and Challenges
A systematic review of over 200 studies concludes that LLMs in recommender systems act as a double-edged sword, creating both opportunities and new risks for trustworthiness.
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Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption
SW-DRSO optimizes a tractable surrogate of worst-case expected loss over plausible inference-time corruptions using a barycentric adversary approximated via simplex weights.
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Safety-Constrained Reinforcement Learning with Post-Training Reachability Verification for Robot Navigation
CVaR-constrained TD3 policies for robot navigation show larger safety margins and higher post-training reachability verification rates than average-cost baselines across simulated scenarios and real-robot tests.
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Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization
Expected regret equals covariance between costs and optimal decisions for linear and quadratic stochastic programs, with explicit bounds on the residual.
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Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
A backup-based safety filter combined with Wasserstein ambiguity sets reduces probabilistic safety certification for nonlinear systems to a one-dimensional search with finite-sample guarantees.
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Ready from Day 1: Population-Aware Coordination for Large-Scale Constrained Multi-Agent Systems
Learned primal and dual maps conditioned on population summaries enable reliable coordination across composition shifts in large multi-agent systems, cutting forecast error 16-19% and violations 20-51% in a supply-cha...
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Ready from Day 1: Population-Aware Coordination for Large-Scale Constrained Multi-Agent Systems
Population-conditioned learned primal and dual maps support reliable coordination of large multi-agent systems under composition shifts without per-cycle retraining, cutting forecast error 16-19% and violations 20-51%...
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Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge
RACER routes between reasoning and non-reasoning LLM judges via constrained distributionally robust optimization to achieve better accuracy-cost trade-offs under distribution shift.
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Q-MMR: Off-Policy Evaluation via Recursive Reweighting and Moment Matching
Q-MMR provides a dimension-free finite-sample guarantee for off-policy evaluation under only Q^π realizability by learning data-point weights inductively via top-down moment matching against a value-function discrimin...
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Q-MMR: Off-Policy Evaluation via Recursive Reweighting and Moment Matching
Q-MMR introduces recursive reweighting and moment matching for off-policy evaluation, delivering dimension-free error bounds under Q^π realizability alone.
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The Distributionally Robust Cyclic Inventory Routing Problem
The authors create a distributionally robust formulation for the cyclic inventory routing problem that admits a deterministic reformulation via multi-point worst-case distributions and chance-constraint equivalents, s...
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Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback
DRRO for RLHF replaces worst-case value with worst-case regret in Wasserstein DRO, producing an exact water-filling solution under l1 ambiguity and a practical sampled-bonus algorithm that reduces proxy over-optimization.
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Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback
DRRO for RLHF minimizes worst-case regret relative to the best policy under Wasserstein reward perturbations, yielding an exact inner solution and water-filling policy structure for the promptwise simplex model plus a...
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Nonsmooth Nonconvex-Concave Minimax Optimization: Convergence Criteria and Algorithms
The authors introduce (ηx,ηy,δ,ε)-GSSP as a convergence criterion and develop projected gradient-free descent-ascent methods achieving non-asymptotic rates for nonsmooth nonconvex-concave minimax optimization without ...
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Distributionally Robust Stochastic MPC under Disturbance-Affine Feedback Policies
A new disturbance-affine distributionally robust MPC framework for uncertain linear systems that is less conservative than tube-based approaches while guaranteeing recursive feasibility and stability.
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Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems
PAC learning-based DR-MPC framework interpolates between robust MPC and stochastic MPC for interactive trajectory planning under agent decision uncertainty.
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The Distributionally Robust Cyclic Inventory Routing Problem
The authors create a distributionally robust formulation for cyclic inventory routing with moment ambiguity, prove a multi-point worst-case distribution, reformulate chance constraints deterministically, and solve via...
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Assured autonomy: How operations research powers and orchestrates generative AI systems
The authors develop a conceptual framework for assured autonomy in generative AI by using flow-based models for auditable generation and adversarial robustness for operational safety, repositioning operations research...
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Multi-Agent Inverse Reinforcement Learning for Identifying Pareto-Efficient Coordination -- A Distributionally Robust Approach
Multi-agent coordination is detected by a feasibility LP, converted to a Type-I-error-controlled detector, and agent utilities are reconstructed with a Wasserstein distributionally robust estimator.
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A Data-embedded Solution Paradigm for Nonconvex Probable Event Constrained Optimization
PECO strengthens chance constraints by mandating feasibility for all high-probability events and is solved via a data-embedded deterministic program that works for nonlinear nonconvex instances when the size of the so...
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Calibrating Decision Robustness via Inverse Conformal Risk Control
A conformal-style estimator certifies simultaneous upper bounds on miscoverage and regret for robust predict-then-optimize policies, tracing a Pareto frontier for choosing the robustness level.
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Target-based Distributionally Robust Minimum Spanning Tree Problem
A target-based DRO model for MST under distributional uncertainty is solved exactly via Benders decomposition and a modified Prim algorithm.
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Breaking the Curse of Repulsion: Remoteness-Aware Control of Negative Off-Policy Updates
The paper derives a 'Divergence Theory' of negative off-policy updates and proposes hard-filtering (DRPO), but the key proof is invalid and the method largely re-implements known top-K/CVaR ideas.
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