Universal AI maximizes Variational Empowerment

Abstract

This paper presents a theoretical framework unifying AIXI -- a model of universal AI -- with variational empowerment as an intrinsic drive for exploration. We build on the existing framework of Self-AIXI -- a universal learning agent that predicts its own actions -- by showing how one of its established terms can be interpreted as a variational empowerment objective. We further demonstrate that universal AI's planning process can be cast as minimizing expected variational free energy (the core principle of active Inference), thereby revealing how universal AI agents inherently balance goal-directed behavior with uncertainty reduction curiosity). Moreover, we argue that power-seeking tendencies of universal AI agents can be explained not only as an instrumental strategy to secure future reward, but also as a direct consequence of empowerment maximization -- i.e. the agent's intrinsic drive to maintain or expand its own controllability in uncertain environments. Our main contribution is to show how these intrinsic motivations (empowerment, curiosity) systematically lead universal AI agents to seek and sustain high-optionality states. We prove that Self-AIXI asymptotically converges to the same performance as AIXI under suitable conditions, and highlight that its power-seeking behavior emerges naturally from both reward maximization and curiosity-driven exploration. Since AIXI can be view as a Bayes-optimal mathematical formulation for Artificial General Intelligence (AGI), our result can be useful for further discussion on AI safety and the controllability of AGI.