  The aim of this work is to address the question of whether we can in
principle design rational decision-making agents or artificial intelligences
embedded in computable physics such that their decisions are optimal in
reasonable mathematical senses. Recent developments in rare event probability
estimation, recursive bayesian inference, neural networks, and probabilistic
planning are sufficient to explicitly approximate reinforcement learners of the
AIXI style with non-trivial model classes (here, the class of resource-bounded
Turing machines). Consideration of the effects of resource limitations in a
concrete implementation leads to insights about possible architectures for
learning systems using optimal decision makers as components.
