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This paper establishes the equivalence between Local Differential Privacy(LDP) and a global limit on learning any knowledge specific to a queriedobject. However, an output from an LDP query is not necessarily required toprovide exact amount of knowledge equal to the upper bound of the learninglimit. The LDP guarantee can overestimate the amount of knowledge gained by ananalyst from some outputs. To address this issue, the least upper bound on theactual knowledge gain is derived and referred to as realized privacy loss. Thismeasure is also shown to serve as an upper bound for the actual g-leakage inquantitative information flow. The gap between the LDP guarantee and realizedprivacy loss motivates the exploration of a more efficient privacy accountingfor fully adaptive composition, where an adversary adaptively selects queriesbased on prior results. The Bayesian Privacy Filter is introduced tocontinuously accept queries until the realized privacy loss of the composedqueries equals the LDP guarantee of the composition, enabling the fullutilization of the privacy budget of an object. The realized privacy loss alsofunctions as a privacy odometer for the composed queries, allowing theremaining privacy budget to accurately represent the capacity to accept newqueries. Additionally, a branch-and-bound method is devised to compute therealized privacy loss when querying against continuous values. Experimentalresults indicate that Bayesian Privacy Filter outperforms the basic compositionby a factor of one to four when composing linear and logistic regressions.

Actual Knowledge Gain as Privacy Loss in Local Privacy Accounting