  This paper establishes the equivalence between Local Differential Privacy
(LDP) and a global limit on learning any knowledge about an object. However, an
output from an LDP query is not necessarily required to provide exact amount of
knowledge equal to the upper bound of the learning limit. Since the amount of
knowledge gain should be proportional to the incurred privacy loss, the
traditional approach of using DP guarantee to measure privacy loss can
occasionally overestimate the actual privacy loss. This is especially
problematic in privacy accounting in LDP, where privacy loss is computed by
accumulating the DP guarantees. To address this issue, this paper introduces
the concept of \textit{realized privacy loss}, which measures the actual
knowledge gained by the analyst after a query, as a more accurate measure of
privacy loss.
  The realized privacy loss is integrated into the privacy accounting of fully
adaptive composition, where an adversary adaptively selects queries based on
previous results. Bayesian Privacy Filter is implemented to continually accept
queries until the realized privacy loss of the composed queries equals the DP
guarantee of the composition, allowing the full utilization of the privacy
budget. Tracking the realized privacy loss during the composition is achieved
through Bayesian Privacy Odometer, and the gap between the privacy budget and
the realized privacy loss measures the leeway of the DP guarantee for future
queries. A branch-and-bound method is devised to enable the Bayesian Privacy
Filter to safeguard objects with continuous values. The Bayesian Privacy Filter
is proven to be at least as efficient as the basic composition, and more
efficient if the queries are privacy-loss compactible. Experimental results
indicate that Bayesian Privacy Filter outperforms the basic composition by a
factor of one to four when composing linear and logistic regressions.
