Bounded-Parameter Partially Observable Markov Decision Processes

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The POMDP is considered as a powerful model for planning under uncertainty. However, it is usually impractical to employ a POMDP with exact parameters to model precisely the real-life situations, due to various reasons such as limited data for learning the model, etc. In this paper, assuming that the parameters of POMDPs are imprecise but bounded, we formulate the framework of bounded-parameter partially observable Markov decision processes (BPOMDPs). A modified value iteration is proposed as a basic strategy for tackling parameter imprecision in BPOMDPs. In addition, we design the UL-based value iteration algorithm, in which each value backup is based on two sets of vectors called U-set and L-set. We propose four typical strategies for setting U-set and L-set, and some of them guarantee that the modified value iteration is implemented through the algorithm. We analyze theoretically the computational complexity and the reward loss of the algorithm. The effectiveness and robustness of the algorithm are revealed by empirical studies.