AIXI Responses to Newcomblike Problems

Abstract

We provide a rigorous analysis of AIXI's behaviour under repeated Newcomblike settings. In this context, a Newcomblike problem is a setting where an agent is tied against an environment that contains a perfect predictor, whose predictions are used to determine the environmet's outputs. Since AIXI lacks good convergence properties, we chose to focus the analysis on determining whether an environment appears computable to AIXI, that is, if it maps actions to observations in a way that a computable program can achieve. It is in this sense that, it turns out, AIXI can learn to one-box in *repeated* Opaque Newcomb, and to smoke in *repeated* Smoking Lesion, but may fail all other Newcomblike problems, because we found no way to reduce them in a computable form. However, we still suspect that AIXI can succeed in the repeated settings.