The complexity of Markov decision processes
Mathematics of Operations Research
Information-based complexity
Motion planning in the presence of movable obstacles
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
On the Probabilistic Foundations of Probabilistic Roadmap Planning
International Journal of Robotics Research
Creating High-quality Paths for Motion Planning
International Journal of Robotics Research
Motion planning for legged and humanoid robots
Motion planning for legged and humanoid robots
The max K-armed bandit: a new model of exploration applied to search heuristic selection
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Finding optimal satisficing strategies for and-or trees
Artificial Intelligence
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Intelligent systems must often reason with partial or corrupted information, due to noisy sensors, limited representation capabilities, and inherent problem complexity. Gathering new information and reasoning with existing information comes at a computational or physical cost. This paper presents a formalism to model systems that solve logical reasoning problems in the presence of uncertainty and priced information. The system is modeled a decision-making agent that moves in a probabilistic belief space, where each information-gathering or computation step changes the belief state. This forms a Markov decision process (MDP), and the belief-optimal system operates according to the belief-space policy that optimizes the MDP. This formalism makes the strong assertion that belief-optimal systems solve the reasoning problem at minimal expected cost, given the background knowledge, sensing capabilities, and computational resources available to the system. Furthermore, this paper argues that belief-optimal systems are more likely to avoid overfitting to benchmarks than benchmark-optimized systems. These concepts are illustrated on a variety of toy problems as well as a path optimization problem encountered in motion planning.