SIAM Review
Bounded-parameter Markov decision process
Artificial Intelligence
Mathematics of Operations Research
Bias and Variance Approximation in Value Function Estimates
Management Science
A New Complexity Result on Solving the Markov Decision Problem
Mathematics of Operations Research
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Operations Research
Dynamic Programming and Optimal Control, Vol. II
Dynamic Programming and Optimal Control, Vol. II
Percentile Optimization for Markov Decision Processes with Parameter Uncertainty
Operations Research
Distributionally Robust Optimization and Its Tractable Approximations
Operations Research
Primal and dual linear decision rules in stochastic and robust optimization
Mathematical Programming: Series A and B
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Markov decision processes MDPs are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use because of their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider robust MDPs that offer probabilistic guarantees in view of the unknown parameters. To this end, we assume that an observation history of the MDP is available. Based on this history, we derive a confidence region that contains the unknown parameters with a prespecified probability 1-β. Afterward, we determine a policy that attains the highest worst-case performance over this confidence region. By construction, this policy achieves or exceeds its worst-case performance with a confidence of at least 1-β. Our method involves the solution of tractable conic programs of moderate size.