On the Computability of AIXI
This addresses foundational theoretical limitations in AI for researchers, but is incremental as it builds on known incomputability results.
The paper tackles the incomputability of the AIXI reinforcement learning agent by quantifying it with the arithmetical hierarchy and proving it is not limit computable, and presents a limit-computable ε-optimal version of AIXI with infinite horizon that maximizes expected rewards.
How could we solve the machine learning and the artificial intelligence problem if we had infinite computation? Solomonoff induction and the reinforcement learning agent AIXI are proposed answers to this question. Both are known to be incomputable. In this paper, we quantify this using the arithmetical hierarchy, and prove upper and corresponding lower bounds for incomputability. We show that AIXI is not limit computable, thus it cannot be approximated using finite computation. Our main result is a limit-computable ε-optimal version of AIXI with infinite horizon that maximizes expected rewards.