  Recent empirical work shows that inconsistent results based on choice of
hyperparameter optimization (HPO) configuration are a widespread problem in ML
research. When comparing two algorithms J and K searching one subspace can
yield the conclusion that J outperforms K, whereas searching another can entail
the opposite. In short, the way we choose hyperparameters can deceive us. We
provide a theoretical complement to this prior work, arguing that, to avoid
such deception, the process of drawing conclusions from HPO should be made more
rigorous. We call this process epistemic hyperparameter optimization (EHPO),
and put forth a logical framework to capture its semantics and how it can lead
to inconsistent conclusions about performance. Our framework enables us to
prove EHPO methods that are guaranteed to be defended against deception, given
bounded compute time budget t. We demonstrate our framework's utility by
proving and empirically validating a defended variant of random search.
