mlsanityData to 14 Oct 2026

Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain

arXiv 2509.14203 ↗First posted 17 Sep 2025math.OC cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward formulations, while natural in many operations research and management contexts, remain underexplored. This is primarily because the dynamic programming foundations are technically challenging and only partially understood, with several fundamental questions remaining open. This paper steps toward a general framework for average-reward robust MDPs by analyzing the constant-gain setting. We study the average-reward robust control problem with possible information asymmetries between the controller and an S-rectangular adversary. Our analysis centers on the constant-gain robust Bellman equation, examining both the existence of solutions and their relationship to the optimal average reward. Specifically, we identify when solutions to the robust Bellman equation characterize the optimal average reward and stationary policies, and we provide one-sided weak communication conditions ensuring solutions' existence. These findings expand the dynamic programming theory for average-reward robust MDPs and lay a foundation for robust dynamic decision making under long-run average criteria in operational environments.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 18 of its 44 references that are in the map. First posted on arXiv 17 Sep 2025.

Builds on

18 of 44 references.

References · 18

  1. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
  3. 2017Online Reinforcement Learning in Stochastic Gamescited by 67
  4. 2023Sharper Model-free Reinforcement Learning for Average-reward Markov Decision Processescited by 29
  5. 2023Robust Average-Reward Markov Decision Processescited by 22
  6. 2023Model-Free Robust Average-Reward Reinforcement Learningcited by 20
  7. 2023On the Foundation of Distributionally Robust Reinforcement Learningcited by 18
  8. 2020First-Order Methods for Wasserstein Distributionally Robust MDPcited by 17
  9. 2023Fast Policy Learning for Linear Quadratic Control with Entropy Regularizationcited by 13
  10. 2023Beyond discounted returns: Robust Markov decision processes with average and Blackwell optimalitycited by 13
  11. 2024An overview of systems-theoretic guarantees in data-driven model predictive controlcited by 3
  12. 2013A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Valuecited by 2
6 more
  1. 2013Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture operatornamemaxmin=operatornamelimvncited by 2
  2. 2024Dynamic Programming-Compatible Uncertainty Sets in Robust Markov Decision Processescited by 2
  3. 2025Playing against a stationary opponentcited by 2
  4. 2017Communicating Zero-Sum Product Stochastic Gamescited by 1
  5. 2019A tutorial on Zero-sum Stochastic Gamescited by 1
  6. 2025Thresholds for sensitive optimality and Blackwell optimality in stochastic gamescited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Non-Rectangular Average-Reward Robust MDPs: Optimal Policies and Their Transient Valuescited by 2
  2. 2026Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterizationcited by 1
  3. 2026Stationary Robust Mean-Field Games under Model Mismatchescited by 0
  4. 2026Vector Bellman Theory for Multichain Robust Average-Reward Markov Decision Processescited by 0
  5. 2026Distributionally Robust Average-Reward Reinforcement Learning: Finite-Sample Guarantees under Weak Communicationcited by 0