  Individual privacy accounting enables bounding differential privacy (DP) loss
individually for each participant involved in the analysis. This can be
informative as often the individual privacy losses are considerably smaller
than those indicated by the DP bounds that are based on considering worst-case
bounds at each data access. In order to account for the individual privacy
losses in a principled manner, we need a privacy accountant for adaptive
compositions of randomised mechanisms, where the loss incurred at a given data
access is allowed to be smaller than the worst-case loss. This kind of analysis
has been carried out for the R\'enyi differential privacy (RDP) by Feldman and
Zrnic (2021), however not yet for the so-called optimal privacy accountants. We
make first steps in this direction by providing a careful analysis using the
Gaussian differential privacy which gives optimal bounds for the Gaussian
mechanism, one of the most versatile DP mechanisms. This approach is based on
determining a certain supermartingale for the hockey-stick divergence and on
extending the R\'enyi divergence-based fully adaptive composition results by
Feldman and Zrnic. We also consider measuring the individual
$(\varepsilon,\delta)$-privacy losses using the so-called privacy loss
distributions. With the help of the Blackwell theorem, we can then make use of
the RDP analysis to construct an approximative individual
$(\varepsilon,\delta)$-accountant.
