  Recently, we have been witnessing an increasing use of machine learning
methods in self-adaptive systems. Machine learning methods offer a variety of
use cases for supporting self-adaptation, e.g., to keep runtime models up to
date, reduce large adaptation spaces, or update adaptation rules. Yet, since
machine learning methods apply in essence statistical methods, they may have an
impact on the decisions made by a self-adaptive system. Given the wide use of
formal approaches to provide guarantees for the decisions made by self-adaptive
systems, it is important to investigate the impact of applying machine learning
methods when such approaches are used. In this paper, we study one particular
instance that combines linear regression to reduce the adaptation space of a
self-adaptive system with statistical model checking to analyze the resulting
adaptation options. We use computational learning theory to determine a
theoretical bound on the impact of the machine learning method on the
predictions made by the verifier. We illustrate and evaluate the theoretical
result using a scenario of the DeltaIoT artifact. To conclude, we look at
opportunities for future research in this area.
