Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Mathematics of Operations Research
Bias and Variance Approximation in Value Function Estimates
Management Science
Optimal Policies for Transshipping Inventory in a Retail Network
Management Science
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Operations Research
Percentile Optimization for Markov Decision Processes with Parameter Uncertainty
Operations Research
Robust Approximation to Multiperiod Inventory Management
Operations Research
Optimality of Affine Policies in Multistage Robust Optimization
Mathematics of Operations Research
Computing robust basestock levels
Discrete Optimization
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Robust dynamic programming robust DP mitigates the effects of ambiguity in transition probabilities on the solutions of Markov decision problems. We consider the computation of robust DP solutions for discrete-stage, infinite-horizon, discounted problems with finite state and action spaces. We present robust modified policy iteration RMPI and demonstrate its convergence. RMPI encompasses both of the previously known algorithms, robust value iteration and robust policy iteration. In addition to proposing exact RMPI, in which the “inner problem” is solved precisely, we propose inexact RMPI, in which the inner problem is solved to within a specified tolerance. We also introduce new stopping criteria based on the span seminorm. Finally, we demonstrate through some numerical studies that RMPI can significantly reduce computation time.