Abstract
In general reinforcement learning, all established optimal agents, including AIXI, are model-based, explicitly maintaining and using environment models. This paper introduces Universal AI with Q-Induction (AIQI), the first model-free agent proven to be asymptotically ε-optimal in general RL. AIQI performs universal induction over distributional action-value functions, instead of policies or environments like previous works. Under a grain of truth condition, we prove that AIQI is strong asymptotically ε-optimal and asymptotically ε-Bayes-optimal. We also apply our novel proof techniques to show asymptotic ε-optimality of Self-AIXI without any ad-hoc assumptions. Our results significantly expand the diversity of known universal agents.