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Online MDP with Transition Prototypes: A Robust Adaptive Approach

arXiv 2412.14075 ↗First posted 18 Dec 2024cs.LGcited by 0

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Abstract (arXiv)

In this work, we consider an online robust Markov Decision Process (MDP) where we have the information of finitely many prototypes of the underlying transition kernel. We consider an adaptively updated ambiguity set of the prototypes and propose an algorithm that efficiently identifies the true underlying transition kernel while guaranteeing the performance of the corresponding robust policy. To be more specific, we provide a sublinear regret of the subsequent optimal robust policy. We also provide an early stopping mechanism and a worst-case performance bound of the value function. In numerical experiments, we demonstrate that our method outperforms existing approaches, particularly in the early stage with limited data. This work contributes to robust MDPs by considering possible prior information about the underlying transition probability and online learning, offering both theoretical insights and practical algorithms for improved decision-making under uncertainty.

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References · 12

  1. 2017Minimax Regret Bounds for Reinforcement Learningcited by 501
  2. 2013(More) Efficient Reinforcement Learning via Posterior Samplingcited by 233
  3. 2019Provably Efficient Exploration in Policy Optimizationcited by 204
  4. 2016Why is Posterior Sampling Better than Optimism for Reinforcement Learning?cited by 116
  5. 2019Learning Adversarial MDPs with Bandit Feedback and Unknown Transitioncited by 85
  6. 2021Sample Complexity of Robust Reinforcement Learning with a Generative Modelcited by 82
  7. 2019Online Convex Optimization in Adversarial Markov Decision Processescited by 79
  8. 2019Corruption-robust exploration in episodic reinforcement learningcited by 72
  9. 2020Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transitioncited by 48
  10. 2022Doubly Robust Distributionally Robust Off-Policy Evaluation and Learningcited by 34
  11. 2017Posterior sampling for reinforcement learning: worst-case regret boundscited by 28
  12. 2020Robust Batch Policy Learning in Markov Decision Processescited by 4

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