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This paper establishes the equivalence between Local Differential Privacy(LDP) and a global limit on learning any knowledge about an object. However, anoutput from an LDP query is not necessarily required to provide exact amount ofknowledge equal to the upper bound of the learning limit. Since the amount ofknowledge gain should be proportional to the incurred privacy loss, thetraditional approach of using DP guarantee to measure privacy loss canoccasionally overestimate the actual privacy loss. This is especiallyproblematic in privacy accounting in LDP, where privacy loss is computed byaccumulating the DP guarantees. To address this issue, this paper introducesthe concept of \textit{realized privacy loss}, which measures the actualknowledge gained by the analyst after a query, as a more accurate measure ofprivacy loss.  The realized privacy loss is integrated into the privacy accounting of fullyadaptive composition, where an adversary adaptively selects queries based onprevious results. Bayesian Privacy Filter is implemented to continually acceptqueries until the realized privacy loss of the composed queries equals the DPguarantee of the composition, allowing the full utilization of the privacybudget. Tracking the realized privacy loss during the composition is achievedthrough Bayesian Privacy Odometer, and the gap between the privacy budget andthe realized privacy loss measures the leeway of the DP guarantee for futurequeries. A branch-and-bound method is devised to enable the Bayesian PrivacyFilter to safeguard objects with continuous values. The Bayesian Privacy Filteris proven to be at least as efficient as the basic composition, and moreefficient if the queries are privacy-loss compactible. Experimental resultsindicate that Bayesian Privacy Filter outperforms the basic composition by afactor of one to four when composing linear and logistic regressions.

Knowledge Gain as Privacy Loss in Local Privacy Accounting