It is a long-standing objective to ease the computation burden incurred by the decision making process. Identification of this mechanisms sensitivity to simplification has tremendous ramifications. Yet, algorithms for decision making under uncertainty usually lean on approximations or heuristics without quantifying their effect. Therefore, challenging scenarios could severely impair the performance of such methods. In this paper, we extend the decision making mechanism to the whole by removing standard approximations and considering all previously suppressed stochastic sources of variability. On top of this extension, our key contribution is a novel framework to simplify decision making while assessing and controlling online the simplifications impact. Furthermore, we present novel stochastic bounds on the return and characterize online the effect of simplification using this framework on a particular simplification technique - reducing the number of samples in belief representation for planning. Finally, we verify the advantages of our approach through extensive simulations.
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