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