  Self-adaptive systems continuously adapt to changes in their execution
environment. Capturing all possible changes to define suitable behaviour
beforehand is unfeasible, or even impossible in the case of unknown changes,
hence human intervention may be required. We argue that adapting to unknown
situations is the ultimate challenge for self-adaptive systems. Learning-based
approaches are used to learn the suitable behaviour to exhibit in the case of
unknown situations, to minimize or fully remove human intervention. While such
approaches can, to a certain extent, generalize existing adaptations to new
situations, there is a number of breakthroughs that need to be achieved before
systems can adapt to general unknown and unforeseen situations. We posit the
research directions that need to be explored to achieve unanticipated
adaptation from the perspective of learning-based self-adaptive systems. At
minimum, systems need to define internal representations of previously unseen
situations on-the-fly, extrapolate the relationship to the previously
encountered situations to evolve existing adaptations, and reason about the
feasibility of achieving their intrinsic goals in the new set of conditions. We
close discussing whether, even when we can, we should indeed build systems that
define their own behaviour and adapt their goals, without involving a human
supervisor.
