Privacy Amplification by Iteration (1808.06651v2)

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.

• The paper introduces 'privacy amplification by iteration,' demonstrating that not revealing intermediate outputs in iterative processes significantly enhances privacy guarantees compared to traditional cumulative accounting or sampling methods.
• The method is applied to noisy stochastic gradient descent (SGD) for convex optimization, showing privacy guarantees comparable to sampling and highlighting reduced per-person privacy loss for data processed earlier.
• This approach has significant implications for distributed and federated learning by potentially reducing communication overhead through less frequent sharing of intermediate results.

Privacy Amplification by Iteration: A Detailed Overview

The paper "Privacy Amplification by Iteration" explores a novel approach to strengthening the privacy guarantees of iterative algorithms used in the context of differential privacy. The authors, Vitaly Feldman, Ilya Mironov, Kunal Talwar, and Abhradeep Thakurta, present a comprehensive analysis of how not revealing intermediate outputs during iterative learning processes can substantially enhance privacy. This paper offers new insights for the field, particularly in relation to stochastic optimization algorithms like noisy stochastic gradient descent (SGD).

The main contribution of the paper is the introduction of "privacy amplification by iteration." Traditional approaches to analyzing privacy loss in iterative algorithms require accounting for the cumulative privacy costs at each step. However, by not disclosing intermediate results, the authors demonstrate that the overall privacy guarantees can be significantly amplified. This insight is particularly relevant for contractive iterative processes where noisy updates are applied repetitively on data points.

Key Contributions

• Iteration-Based Privacy Amplification: The authors develop a formal analysis showing that the cumulative privacy cost can be lower when intermediate steps are not released. This method contrasts with privacy-amplification-by-sampling, which involves secret random selection of data subsets.
• Application to Noisy SGD: The framework is applied to convex optimization tasks using noisy stochastic gradient descent. The authors highlight that inserting noise in each iteration, coupled with contractive updates, can achieve privacy guarantees comparable to those of sampling-based amplification techniques.
• Per-Person Privacy Understanding: The approach not only provides a reduced aggregate privacy budget but also underscores that privacy loss varies among individuals. Specifically, earlier data points in an iterative sequence experience less privacy loss compared to those processed later.
• Distributed Learning and Communication Efficiency: The findings have implications for distributed learning frameworks. By reducing the need for intermediate result sharing, the methods can lead to lower communication overhead and are suited for federated learning settings where minimizing communication is crucial.

Numerical and Theoretical Implications

The authors present several experimental results and theoretical proofs to substantiate their claims. They emphasize that the privacy guarantees become particularly strong when the order of processing is fixed, as opposed to randomly sampled or continually varied. For instance, with $n$ data points, it becomes viable to execute $O(n)$ optimizations at nearly the cost of one by leveraging the weakened privacy constraints for early points.

Speculative Outlook

The proposed method points to several promising future directions in differential privacy:

• Algorithm Design for Federated Learning: Privacy amplification by iteration can inspire new privacy-conscious algorithm designs that are efficient for decentralized systems.
• Multi-Query Scenarios: The technique can be generalized to handle multiple queries on the same data, which is notably beneficial for scenarios involving repeated data analysis tasks.
• Hybrid Approaches: Integrating this iterative method with other privacy-preserving strategies can yield hybrid approaches that balance better between utility and privacy.

Conclusion

This work by Feldman et al. provides a substantial addition to differential privacy research. By moving away from conventional intermediate outcome disclosure, the paper points to innovative methods for achieving robust privacy protections in iterative learning. The paper paves the way for future explorations into optimization algorithms' design and analysis under privacy constraints, especially in the context of distributed and federated learning systems. As data privacy continues to be paramount, such influential studies contribute significantly to the development of secure algorithmic frameworks.