  Learning a good state representation is a critical skill when dealing with
multiple tasks in Reinforcement Learning as it allows for transfer and better
generalization between tasks. However, defining what constitute a useful
representation is far from simple and there is so far no standard method to
find such an encoding. In this paper, we argue that distillation -- a process
that aims at imitating a set of given policies with a single neural network --
can be used to learn a state representation displaying favorable
characteristics. In this regard, we define three criteria that measure
desirable features of a state encoding: the ability to select important
variables in the input space, the ability to efficiently separate states
according to their corresponding optimal action, and the robustness of the
state encoding on new tasks. We first evaluate these criteria and verify the
contribution of distillation on state representation on a toy environment based
on the standard inverted pendulum problem, before extending our analysis on
more complex visual tasks from the Atari and Procgen benchmarks.
