Online MDP with Transition Prototypes: A Robust Adaptive Approach
This work addresses robust decision-making under uncertainty for applications like robotics or finance, but it is incremental as it builds on prior robust MDP frameworks by incorporating online learning with prototypes.
The paper tackles the problem of online robust Markov Decision Processes (MDPs) with transition prototypes by proposing an algorithm that identifies the true transition kernel and guarantees robust policy performance, achieving sublinear regret and outperforming existing methods in early-stage experiments.
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.