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 belief-dependent 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 belief-dependent 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.

研究了基于信念空间规划的在线决策问题，在信息收集等场景下，介绍了一种自适应的方法来寻求最大可行回报，应用这种方法可以在保证准确率的前提下显著加速在线决策过程，并进行了大量现实模拟来验证此方法的优越性。

自适应概率信赖约束下的连续高维信念空间规划

Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints

One of the most complex tasks of decision making and planning is to gather
information. This task becomes even more complex when the state is
high-dimensional and its belief cannot be expressed with a parametric
distribution. Although the state is high-dimensional, in many problems only a
small fraction of it might be involved in transitioning the state and
generating observations. We exploit this fact to calculate an
information-theoretic expected reward, mutual information (MI), over a much
lower-dimensional subset of the state, to improve efficiency and without
sacrificing accuracy. A similar approach was used in previous works, yet
specifically for Gaussian distributions, and we here extend it for general
distributions. Moreover, we apply the dimensionality reduction for cases in
which the new states are augmented to the previous, yet again without
sacrificing accuracy. We then continue by developing an estimator for the MI
which works in a Sequential Monte Carlo (SMC) manner, and avoids the
reconstruction of future belief's surfaces. Finally, we show how this work is
applied to the informative planning optimization problem. This work is then
evaluated in a simulation of an active SLAM problem, where the improvement in
both accuracy and timing is demonstrated.

本文提出一种计算信息论预期奖励的方法，运用信息量 (mutual information) 进行降维，开发出一个 Sequential Monte Carlo (SMC) 估计器，以避免未来信仰表面的重建，并将此方法应用于信息规划优化问题，最后在活动 SLAM 问题的模拟中评估该方法。