  Many important real-world problems have action spaces that are
high-dimensional, continuous or both, making full enumeration of all possible
actions infeasible. Instead, only small subsets of actions can be sampled for
the purpose of policy evaluation and improvement. In this paper, we propose a
general framework to reason in a principled way about policy evaluation and
improvement over such sampled action subsets. This sample-based policy
iteration framework can in principle be applied to any reinforcement learning
algorithm based upon policy iteration. Concretely, we propose Sampled MuZero,
an extension of the MuZero algorithm that is able to learn in domains with
arbitrarily complex action spaces by planning over sampled actions. We
demonstrate this approach on the classical board game of Go and on two
continuous control benchmark domains: DeepMind Control Suite and Real-World RL
Suite.
