Privacy Amplification by Iteration

TL;DR

This paper shows that for contractive iterative algorithms, not releasing intermediate results significantly enhances privacy guarantees, enabling better privacy-utility trade-offs in convex optimization with differential privacy.

Contribution

It introduces a novel privacy amplification technique for contractive iterations that does not rely on releasing intermediate results, improving privacy guarantees in iterative algorithms.

Findings

Non-private data points can reduce privacy gap in convex optimization.

Strong privacy amplification achieved without releasing intermediate results.

Comparable guarantees to privacy-amplification-by-sampling in new settings.

Abstract

Many commonly used learning algorithms work by iteratively updating an intermediate solution using one or a few data points in each iteration. Analysis of differential privacy for such algorithms often involves ensuring privacy of each step and then reasoning about the cumulative privacy cost of the algorithm. This is enabled by composition theorems for differential privacy that allow releasing of all the intermediate results. In this work, we demonstrate that for contractive iterations, not releasing the intermediate results strongly amplifies the privacy guarantees. We describe several applications of this new analysis technique to solving convex optimization problems via noisy stochastic gradient descent. For example, we demonstrate that a relatively small number of non-private data points from the same distribution can be used to close the gap between private and non-private convex optimization. In addition, we demonstrate that we can achieve guarantees similar to those obtainable using the privacy-amplification-by-sampling technique in several natural settings where that technique cannot be applied.