It is a long-standing objective to ease the computation burden incurred by the decision making process. Identification of this mechanism's 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 simplification's 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.
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings, calculating an optimal course of action inflicts an enormous computational burden on the agent. Moreover, in many scenarios, e.g., information gathering, it is required to introduce a beliefdependent constraint. Prompted by this demand, in this paper, we consider a recently introduced probabilistic belief-dependent constrained POMDP. We present a technique to adaptively accept or discard a candidate action sequence with respect to a probabilistic belief-dependent constraint, before expanding a complete set of future observations samples and without any loss in accuracy. Moreover, using our proposed framework, we contribute an adaptive method to find a maximal feasible return (e.g., information gain) in terms of Value at Risk for the candidate action sequence with substantial acceleration. On top of that, we introduce an adaptive simplification technique for a probabilistically constrained setting. Such an approach provably returns an identical-quality solution while dramatically accelerating online decision making. Our universal framework applies to any beliefdependent constrained continuous POMDP with parametric beliefs, as well as nonparametric beliefs represented by particles. In the context of an information-theoretic constraint, our presented framework stochastically quantifies if a cumulative information gain along the planning horizon is sufficiently significant (e.g. for, information gathering, active SLAM). We apply our method to active SLAM, a highly challenging problem of high dimensional Belief Space Planning. Extensive realistic simulations corroborate the superiority of our proposed ideas.
It is a long-standing objective to ease the computation burden incurred by the decision-making problem under partial observability. Identifying the sensitivity to simplification of various components of the original problem 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, we scrutinize the distribution of the return. We begin from a return given a single candidate policy and continue to the pair of returns given a corresponding pair of candidate policies. Furthermore, we present novel stochastic bounds on the return and novel tools, Probabilistic Loss (PLoss) and its online accessible counterpart (PbLoss), to characterize the effect of a simplification.
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