Optimal adaptive policies for Markov decision processes
Mathematics of Operations Research
Bounded-parameter Markov decision process
Artificial Intelligence
Dynamic Programming and Optimal Control, Two Volume Set
Dynamic Programming and Optimal Control, Two Volume Set
R-max - a general polynomial time algorithm for near-optimal reinforcement learning
The Journal of Machine Learning Research
A theoretical analysis of Model-Based Interval Estimation
ICML '05 Proceedings of the 22nd international conference on Machine learning
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Operations Research
Reachability analysis of uncertain systems using bounded-parameter Markov decision processes
Artificial Intelligence
Near-optimal Regret Bounds for Reinforcement Learning
The Journal of Machine Learning Research
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Bounded parameter Markov Decision Processes (BMDPs) address the issue of dealing with uncertainty in the parameters of a Markov Decision Process (MDP). Unlike the case of an MDP, the notion of an optimal policy for a BMDP is not entirely straightforward. We consider two notions of optimality based on optimistic and pessimistic criteria. These have been analyzed for discounted BMDPs. Here we provide results for average reward BMDPs. We establish a fundamental relationship between the discounted and the average reward problems, prove the existence of Blackwell optimal policies and, for both notions of optimality, derive algorithms that converge to the optimal value function.