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The goal of this PR is to allow initializing multiple mechanisms when they are to be applied simultaneously with a single total privacy budget, usage will be with the JointMechanism class.
When the total (epsilon, delta) budget has been provided we compute the noise parameter for each mechanism as follows:
Suppose we have two mechanisms [M1, M2] (self composed over n steps). The user provides a list budget_proportions [p1, p2], which gives the proportion of the total budget each mechanism is allocated. We then find large_epsilon and noise parameters [s1, s2] such that
This is done in practice with (nested) binary searches, the outer for large_epsilon and the inner for the noise parameters s1 and s2.