  Composition is a key feature of differential privacy. Well-known advanced
composition theorems allow one to query a private database quadratically more
times than basic privacy composition would permit. However, these results
require that the privacy parameters of all algorithms be fixed before
interacting with the data. To address this, Rogers et al. introduced fully
adaptive composition, wherein both algorithms and their privacy parameters can
be selected adaptively. They defined two probabilistic objects to measure
privacy in adaptive composition: privacy filters, which provide differential
privacy guarantees for composed interactions, and privacy odometers,
time-uniform bounds on privacy loss. There are substantial gaps between
advanced composition and existing filters and odometers. First, existing
filters place stronger assumptions on the algorithms being composed. Second,
these odometers and filters suffer from large constants, making them
impractical. We construct filters that match the rates of advanced composition,
including constants, despite allowing for adaptively chosen privacy parameters.
En route we also derive a privacy filter for approximate zCDP. We also
construct several general families of odometers. These odometers match the
tightness of advanced composition at an arbitrary, preselected point in time,
or at all points in time simultaneously, up to a doubly-logarithmic factor. We
obtain our results by leveraging advances in martingale concentration. In sum,
we show that fully adaptive privacy is obtainable at almost no loss.
