  A parameterized skill is a mapping from multiple goals/task parameters to the
policy parameters to accomplish them. Existing works in the literature show how
a parameterized skill can be learned given a task space that defines all the
possible achievable goals. In this work, we focus on tasks defined in terms of
final states (goals), and we face on the challenge where the agent aims to
autonomously acquire a parameterized skill to manipulate an initially unknown
environment. In this case, the task space is not known a priori and the agent
has to autonomously discover it. The agent may posit as a task space its whole
sensory space (i.e. the space of all possible sensor readings) as the
achievable goals will certainly be a subset of this space. However, the space
of achievable goals may be a very tiny subspace in relation to the whole
sensory space, thus directly using the sensor space as task space exposes the
agent to the curse of dimensionality and makes existing autonomous skill
acquisition algorithms inefficient. In this work we present an algorithm that
actively discovers the manifold of the achievable goals within the sensor
space. We validate the algorithm by employing it in multiple different
simulated scenarios where the agent actions achieve different types of goals:
moving a redundant arm, pushing an object, and changing the color of an object.
