Differentially Private Simple Genetic Algorithms

Abstract

We study the differentially private (DP) selection problem, where the goal is to select an item from a set of candidates that approximately maximizes a given objective function. The most common solution to this problem is to use the exponential mechanism. The issue with this approach is that the exponential mechanism must compute the objective function for all possible candidates in the domain. For many real-world problems, the length of the domain is exponential, making this approach impractical. Genetic algorithms (GAs) use the principles of evolution in nature to efficiently search through large domains and find the best candidate. However, current work applying DP to GAs exhibits poor utility and the results are difficult to reproduce.

This work provides a new DP GA based on the popular simple genetic algorithm from the non-private literature. The biggest challenge is the number of selections made in the simple GA, each consuming a part of the privacy budget under DP. Our design reduces the number of selections and takes advantage of advanced composition techniques to overcome this challenge without impeding the heuristics that make the simple GA effective. We evaluate our solution over four different datasets using both convex and non-convex problems. The results demonstrate that our GA outperforms previous work in DP GAs as well as DP local search techniques. We further show that our DP GA offers increased utility across different datasets for efficiently scaling the exponential mechanism to large domains. Finally, we demonstrate that our general solution is competitive in utility or efficiency with state-of-the-art problem-specific solutions.