Convergence of Expected Utilities with Algorithmic Probability Distributions
Abstract
We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable and compatible with a finite set of known inputoutput pairs, and the agent assigns a positive probability to each such hypothesis. We do not require that this probability distribution be computable, but it must be bounded below by a positive computable function. The agent has a utility function on outputs from the environment. We show that if this utility function is bounded below in absolute value by an unbounded computable function, then the expected utility of any input is undefined. This implies that a computable utility function will have convergent expected utilities iff that function is bounded.
 Publication:

arXiv eprints
 Pub Date:
 December 2007
 DOI:
 10.48550/arXiv.0712.4318
 arXiv:
 arXiv:0712.4318
 Bibcode:
 2007arXiv0712.4318D
 Keywords:

 Computer Science  Artificial Intelligence
 EPrint:
 2 pages + title page, references