Convergence of Expected Utility for Universal AI

07/31/2009

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by   Peter de Blanc, et al.

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We consider a sequence of repeated interactions between an agent and an environment. Uncertainty about the environment is captured by a probability distribution over a space of hypotheses, which includes all computable functions. Given a utility function, we can evaluate the expected utility of any computational policy for interaction with the environment. After making some plausible assumptions (and maybe one not-so-plausible assumption), we show that if the utility function is unbounded, then the expected utility of any policy is undefined.