Kris Hauser
ABSTRACT
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.
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