Simplification for Efficient Decision Making Under Uncertainty with General Distributions

Planning under uncertainty in partially observable domains, also known as Belief Space Planning (BSP), is an essential scientific inquiry to create Artificial Intelligence and a recurrent aspect in many real-life scenarios. The prevailing way to formulate such a decision making is the Partially Observable Markov Decision Process (POMDP). The POMDP is notoriously hard to solve due to the multitude of possible future robot actions and observations along the planning horizon.

In this research, we address the problem of efficient online BSP in continuous domains. Towards this end, we first introduce the adaptive multilevel simplification paradigm, which aims to accelerate decision-making while providing performance guarantees. We then suggest a novel Probabilistic POMDP formulation that takes into account the variability of the POMDP elements stemming from nonparametric representations. Based on this extension we formulate stochastic bounds over the cumulative robot reward and perform risk-aware BSP efficiently considering state-dependent rewards and information-theoretic rewards, such as differential entropy. In this work, we suggest an adaptive scheme to evaluate the theoretical differential entropy over a general belief surface. Finally, we focus on Constrained POMDP. Here, we propose a novel Probabilistically Constrained belief-dependent POMDP. Our constraint operator is belief-dependent for the first time to the best of our knowledge. It can be information related in the context of exploration or motivated by safety aspects. In both settings, we accelerate online planning while providing guarantees on the impact of the acceleration.