Model-Based Planning with Discrete and Continuous Actions
  Action planning using learned and differentiable forward models of the world
is a general approach which has a number of desirable properties, including
improved sample complexity over model-free RL methods, reuse of learned models
across different tasks, and the ability to perform efficient gradient-based
optimization in continuous action spaces. However, this approach does not apply
straightforwardly when the action space is discrete. In this work, we show that
it is in fact possible to effectively perform planning via backprop in discrete
action spaces, using a simple paramaterization of the actions vectors on the
simplex combined with input noise when training the forward model. Our
experiments show that this approach can match or outperform model-free RL and
discrete planning methods on gridworld navigation tasks in terms of performance
and/or planning time while using limited environment interactions, and can
additionally be used to perform model-based control in a challenging new task
where the action space combines discrete and continuous actions. We furthermore
propose a policy distillation approach which yields a fast policy network which
can be used at inference time, removing the need for an iterative planning
procedure.
