Algorithms : Multiplicative Weights
نویسنده
چکیده
We'll recall (again) some definitions from last time: Definition 1 (Database Update Sequence) Let D ∈ N |X | be any database and let Using the exponential mechanism as a distinguisher, we proved the following utility theorem about the IC mechanism: Theorem 3 Given a B(α)-DUA, the Iterative Construction mechanism is (α, β) accurate and-differentially private for: α ≥ 8B(α/2) nn log C γ and (, δ)-differentially private for: α ≥ 16 B(α/2) log(1/δ) nn log C γ so long as γ ≤ β/(2B(α/2)). We plugged in the Median Mechanism, based on the existence of small nets, to get: Plugging this in to the IC mechanism, we get: Theorem 4 Instantiated with the median mechanim, the Iterative Construction mechanism is (α, β) accurate and-differentially private for:
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The Multiplicative Weights Update Method: a Meta-Algorithm and Applications
Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simple instantiations of the meta algorithm.
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