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Inverse Optimization: Theory and Applications

arXiv 2109.03920 ↗First posted 8 Sep 2021math.OCcited by 48

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Abstract (arXiv)

Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization takes decisions as input and determines an objective and/or constraints that render these decisions approximately or exactly optimal. In recent years, there has been an explosion of interest in the mathematics and applications of inverse optimization. This paper provides a comprehensive review of both the methodological and application-oriented literature in inverse optimization.

Key facts. Cited by 48 papers in the map (data through 14 Oct 2026). First posted on arXiv 8 Sep 2021.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 10; 2025: 15; 2026: 19.

48 papers.

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  1. 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 82
  2. 2025Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agentscited by 40
  3. 2025Network Diffuser for Placing-Scheduling Service Function Chains with Inverse Demonstrationcited by 11
  4. 2023Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithmscited by 10
  5. 2025Online Inverse Linear Optimization: Efficient Logarithmic-Regret Algorithm, Robustness to Suboptimality, and Lower Boundcited by 9
  6. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  7. 2025Revisiting Online Learning Approach to Inverse Linear Optimization: A Fenchel-Young Loss Perspective and Gap-Dependent Regret Analysiscited by 8
  8. 2026Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex Action Setscited by 8
  9. 2026Simple Projection-Free Algorithm for Contextual Recommendation with Logarithmic Regret and Robustnesscited by 6
  10. 2026Tight Generalization Bounds for Noiseless Inverse Optimizationcited by 6
  11. 2023Inverse Optimization for Routing Problemscited by 5
  12. 2025ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problemscited by 5
36 more
  1. 2025Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)cited by 5
  2. 2023Data-driven decision-focused surrogate modelingcited by 4
  3. 2024Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methodscited by 4
  4. 2024Offline Hierarchical Reinforcement Learning via Inverse Optimizationcited by 4
  5. 2026Optimal Decision-Making Based on Prediction Setscited by 4
  6. 2024From Inverse Optimization to Feasibility to ERMcited by 3
  7. 2024Counterfactual Explanations for Linear Optimizationcited by 3
  8. 2024BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantificationcited by 3
  9. 2024Scalable Kernel Inverse Optimizationcited by 3
  10. 2025Efficient Inverse Multiagent Learningcited by 3
  11. 2025Conformalized Decision Risk Assessmentcited by 3
  12. 2026Efficient Online Inverse Optimization with O(d) Regretcited by 3
  13. 2024Block Sparse Bayesian Learning: A Diversified Schemecited by 2
  14. 2025Inverse Mixed-Integer Programming: Learning Constraints then Objective Functionscited by 2
  15. 2026Conformal Risk-Averse Decision Making with Action Conditional Guaranteecited by 2
  16. 2026Bilevel Optimization for Neural Architecture Searchcited by 2
  17. 2026Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programscited by 2
  18. 2026Tight Regret Bound for Online Inverse Linear Optimization via Multiscale Matrix Weightscited by 2
  19. 2024Solving 0-1 Integer Programs with Unknown Knapsack Constraints Using Membership Oraclescited by 1
  20. 2024Estimating the Unobservable Components of Electricity Demand Response with Inverse Optimizationcited by 1
  21. 2025Apprenticeship learning with prior beliefs using inverse optimizationcited by 1
  22. 2025Frugal Machine Learning for Energy-efficient, and Resource-aware Artificial Intelligencecited by 1
  23. 2024Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximizationcited by 0
  24. 2025A Fenchel-Young Loss Approach to Data-Driven Inverse Optimizationcited by 0
  25. 2025Preference Elicitation for Multi-objective Combinatorial Optimization with Active Learning and Maximum Likelihood Estimationcited by 0
  26. 2025Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Gamescited by 0
  27. 2026Behavior Learning (BL): Learning Hierarchical Optimization Structures from Datacited by 0
  28. 2026Contextual Preference Distribution Learningcited by 0
  29. 2026Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimizationcited by 0
  30. 2026A2utoLPBench: An Auto-Generated, Agent-Friendly LP Benchmark via Inverse-KKT Constructioncited by 0
  31. 2026Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensorscited by 0
  32. 2026A Multi-stage Constrained Optimization Framework for Data-driven Problemscited by 0
  33. 2026Uncovering expert objectives in production planning via inverse optimization: An industrial case studycited by 0
  34. 2026Decision-Driven Regularization: A Blended Model for Learning and Optimizationcited by 0
  35. 2026The Value of Human Expertisecited by 0
  36. 2026TACIT: Optimization Models that Learn from Their Mistakescited by 0