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Distributionally Robust Counterpart in Markov Decision Processes

arXiv 1501.07418 ↗First posted 29 Jan 2015eess.SY cs.SY math.OCcited by 33

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Abstract (arXiv)

This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and seeks the strategy which maximizes the expected performance under the most adversarial distribution. In particular, we generalize previous study citexu2012distributionally which concentrates on distribution sets with very special structure to much more generic class of distribution sets, and show that the optimal strategy can be obtained efficiently under mild technical condition. This significantly extends the applicability of distributionally robust MDP to incorporate probabilistic information of uncertainty in a more flexible way.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Jan 2015.

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Citing papers per year: 2021: 2; 2022: 9; 2023: 12; 2024: 6; 2025: 3; 2026: 1.

33 papers.

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  1. 2022Robust Reinforcement Learning using Offline Datacited by 96
  2. 2021Sample Complexity of Robust Reinforcement Learning with a Generative Modelcited by 83
  3. 2022Policy Gradient Method For Robust Reinforcement Learningcited by 69
  4. 2023Improved Sample Complexity Bounds for Distributionally Robust Reinforcement Learningcited by 44
  5. 2022Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizabilitycited by 36
  6. 2021On the Optimality of Batch Policy Optimization Algorithmscited by 28
  7. 2024Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximationcited by 25
  8. 2023Robust Average-Reward Markov Decision Processescited by 22
  9. 2023Replicable Reinforcement Learningcited by 21
  10. 2023Model-Free Robust Average-Reward Reinforcement Learningcited by 20
  11. 2024Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learningcited by 18
  12. 2023Soft Robust MDPs and Risk-Sensitive MDPs: Equivalence, Policy Gradient, and Sample Complexitycited by 17
21 more
  1. 2023Distributionally Robust Model-based Reinforcement Learning with Large State Spacescited by 17
  2. 2024Upper and Lower Bounds for Distributionally Robust Off-Dynamics Reinforcement Learningcited by 16
  3. 2022Robust Constrained Reinforcement Learningcited by 15
  4. 2024Distributionally Robust Constrained Reinforcement Learning under Strong Dualitycited by 15
  5. 2023Risk-Averse Model Uncertainty for Distributionally Robust Safe Reinforcement Learningcited by 12
  6. 2022On the convex formulations of robust Markov decision processescited by 10
  7. 2023Optimal Transport Perturbations for Safe Reinforcement Learning with Robustness Guaranteescited by 9
  8. 2022Group Distributionally Robust Reinforcement Learning with Hierarchical Latent Variablescited by 7
  9. 2025Confounding Robust Deep Reinforcement Learning: A Causal Approachcited by 7
  10. 2023Risk-Averse Reinforcement Learning via Dynamic Time-Consistent Risk Measurescited by 5
  11. 2025DR-SAC: Distributionally Robust Soft Actor-Critic for Reinforcement Learning under Uncertaintycited by 3
  12. 2023Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Controlcited by 2
  13. 2024Sequential Decision-Making under Uncertainty: A Robust MDPs reviewcited by 2
  14. 2022Robust Phi-Divergence MDPscited by 1
  15. 2025DR-PETS: Learning-Based Control With Planning in Adversarial Environmentscited by 1
  16. 2022User-Oriented Robust Reinforcement Learningcited by 0
  17. 2022Set-based value operators for non-stationary Markovian environmentscited by 0
  18. 2023Risk-Averse MDPs under Reward Ambiguitycited by 0
  19. 2023On Practical Robust Reinforcement Learning: Practical Uncertainty Set and Double-Agent Algorithmcited by 0
  20. 2024Robust Offline Reinforcement Learning for Non-Markovian Decision Processescited by 0
  21. 2026Robust Transfer Learning with Side Informationcited by 0