  After initial release of a machine learning algorithm, the model can be
fine-tuned by retraining on subsequently gathered data, adding newly discovered
features, or more. Each modification introduces a risk of deteriorating
performance and must be validated on a test dataset. It may not always be
practical to assemble a new dataset for testing each modification, especially
when most modifications are minor or are implemented in rapid succession.
Recent works have shown how one can repeatedly test modifications on the same
dataset and protect against overfitting by (i) discretizing test results along
a grid and (ii) applying a Bonferroni correction to adjust for the total number
of modifications considered by an adaptive developer. However, the standard
Bonferroni correction is overly conservative when most modifications are
beneficial and/or highly correlated. This work investigates more powerful
approaches using alpha-recycling and sequentially-rejective graphical
procedures (SRGPs). We introduce novel extensions that account for correlation
between adaptively chosen algorithmic modifications. In empirical analyses, the
SRGPs control the error rate of approving unacceptable modifications and
approve a substantially higher number of beneficial modifications than previous
approaches.
