  Many state-of-the-art reinforcement learning (RL) algorithms typically assume
that the environment is an ergodic Markov Decision Process (MDP). In contrast,
the field of universal reinforcement learning (URL) is concerned with
algorithms that make as few assumptions as possible about the environment. The
universal Bayesian agent AIXI and a family of related URL algorithms have been
developed in this setting. While numerous theoretical optimality results have
been proven for these agents, there has been no empirical investigation of
their behavior to date. We present a short and accessible survey of these URL
algorithms under a unified notation and framework, along with results of some
experiments that qualitatively illustrate some properties of the resulting
policies, and their relative performance on partially-observable gridworld
environments. We also present an open-source reference implementation of the
algorithms which we hope will facilitate further understanding of, and
experimentation with, these ideas.
