mlsanityData to 7 Oct 2026

Qualitative Analysis of ω-Regular Objectives on Robust MDPs

arXiv 2505.04539 ↗First posted 7 May 2025cs.AIcited by 2

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Abstract (arXiv)

Robust Markov Decision Processes (RMDPs) generalize classical MDPs that consider uncertainties in transition probabilities by defining a set of possible transition functions. An objective is a set of runs (or infinite trajectories) of the RMDP, and the value for an objective is the maximal probability that the agent can guarantee against the adversarial environment. We consider (a) reachability objectives, where given a target set of states, the goal is to eventually arrive at one of them; and (b) parity objectives, which are a canonical representation for ω-regular objectives. The qualitative analysis problem asks whether the objective can be ensured with probability 1. In this work, we study the qualitative problem for reachability and parity objectives on RMDPs without making any assumption over the structures of the RMDPs, e.g., unichain or aperiodic. Our contributions are twofold. We first present efficient algorithms with oracle access to uncertainty sets that solve qualitative problems of reachability and parity objectives. We then report experimental results demonstrating the effectiveness of our oracle-based approach on classical RMDP examples from the literature scaling up to thousands of states.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 41 references that are in the map. First posted on arXiv 7 May 2025.

Builds on

14 of 41 references.

References · 14

  1. 2021Online Robust Reinforcement Learning with Model Uncertaintycited by 95
  2. 2019Reinforcement Learning for Temporal Logic Control Synthesis with Probabilistic Satisfaction Guaranteescited by 77
  3. 2022Policy Gradient Method For Robust Reinforcement Learningcited by 67
  4. 2021Compositional Reinforcement Learning from Logical Specificationscited by 65
  5. 2020Partial Policy Iteration for L1-Robust Markov Decision Processescited by 49
  6. 2022Policy Gradient in Robust MDPs with Global Convergence Guaranteecited by 35
  7. 2023Robust Average-Reward Markov Decision Processescited by 22
  8. 2024Robust Markov Decision Processes: A Place Where AI and Formal Methods Meetcited by 18
  9. 2023On Dynamic Programming Decompositions of Static Risk Measures in Markov Decision Processescited by 17
  10. 2023Reducing Blackwell and Average Optimality to Discounted MDPs via the Blackwell Discount Factorcited by 13
  11. 2023Beyond discounted returns: Robust Markov decision processes with average and Blackwell optimalitycited by 12
  12. 2024Solving Robust Markov Decision Processes: Generic, Reliable, Efficientcited by 11
2 more
  1. 2020The Complexity of Reachability in Parametric Markov Decision Processescited by 10
  2. 2023Solving Long-run Average Reward Robust MDPs via Stochastic Gamescited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Solving Robust POMDPs with Omega-regular Objectives via Partially Observable Stochastic Gamescited by 0
  2. 2026Quantitative Analysis of ω-Regular Robust MDPscited by 0