  Reinforcement learning (RL) combines a control problem with statistical
estimation: The system dynamics are not known to the agent, but can be learned
through experience. A recent line of research casts `RL as inference' and
suggests a particular framework to generalize the RL problem as probabilistic
inference. Our paper surfaces a key shortcoming in that approach, and clarifies
the sense in which RL can be coherently cast as an inference problem. In
particular, an RL agent must consider the effects of its actions upon future
rewards and observations: The exploration-exploitation tradeoff. In all but the
most simple settings, the resulting inference is computationally intractable so
that practical RL algorithms must resort to approximation. We demonstrate that
the popular `RL as inference' approximation can perform poorly in even very
basic problems. However, we show that with a small modification the framework
does yield algorithms that can provably perform well, and we show that the
resulting algorithm is equivalent to the recently proposed K-learning, which we
further connect with Thompson sampling.
