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The aim of this work is to address the question of whether we can inprinciple design rational decision-making agents or artificial intelligencesembedded in computable physics such that their decisions are optimal inreasonable mathematical senses. Recent developments in rare event probabilityestimation, recursive bayesian inference, neural networks, and probabilisticplanning are sufficient to explicitly approximate reinforcement learners of theAIXI style with non-trivial model classes (here, the class of resource-boundedTuring machines). Consideration of the effects of resource limitations in aconcrete implementation leads to insights about possible architectures forlearning systems using optimal decision makers as components.

A Monte Carlo Algorithm for Universally Optimal Bayesian Sequence Prediction and Planning