  In its quest for approaches to taming uncertainty in self-adaptive systems
(SAS), the research community has largely focused on solutions that adapt the
SAS architecture or behaviour in response to uncertainty. By comparison,
solutions that reduce the uncertainty affecting SAS (other than through the
blanket monitoring of their components and environment) remain underexplored.
Our paper proposes a more nuanced, adaptive approach to SAS uncertainty
reduction. To that end, we introduce a SAS architecture comprising an
uncertainty reduction controller that drives the adaptive acquisition of new
information within the SAS adaptation loop, and a tool-supported method that
uses probabilistic model checking to synthesise such controllers. The
controllers generated by our method deliver optimal trade-offs between SAS
uncertainty reduction benefits and new information acquisition costs. We
illustrate the use and evaluate the effectiveness of our approach for mobile
robot navigation and server infrastructure management SAS.
