Together or Alone: The Price of Privacy in Collaborative Learning

Abstract

Machine learning algorithms have reached mainstream status and are widely deployed in many applications. The accuracy of such algorithms depends significantly on the size of the underlying training dataset; in reality a small or medium sized organization often does not have the necessary data to train a reasonably accurate model. For such organizations, a realistic solution is to train their machine learning models based on their joint dataset (which is a union of the individual ones). Unfortunately, privacy concerns prevent them from straightforwardly doing so. While a number of privacy-preserving solutions exist for collaborating organizations to securely aggregate the parameters in the process of training the models, we are not aware of any work that provides a rational framework for the participants to precisely balance the privacy loss and accuracy gain in their collaboration. In this paper, by focusing on a two-player setting, we model the collaborative training process as a two-player game where each player aims to achieve higher accuracy while preserving the privacy of its own dataset. We introduce the notion of Price of Privacy, a novel approach for measuring the impact of privacy protection on the accuracy in the proposed framework. Furthermore, we develop a game-theoretical model for different player types, and then either find or prove the existence of a Nash Equilibrium with regard to the strength of privacy protection for each player. Using recommendation systems as our main use case, we demonstrate how two players can make practical use of the proposed theoretical framework, including setting up the parameters and approximating the non-trivial Nash Equilibrium.

The Price of Privacy in Collaborative Learning

“…On the practical side, we studied a Recommendation System use case: we applied two different privacy-preserving mechanisms on two real-world datasets and confirmed via experiments that the assumption which ensures the existence of a NE holds. Complementary to the CoL game, we interpolated Φ for our use case, and devised a possible way to approximate it in real-world scenarios [7].…”

“…To break this loop, we propose an approach called Self-Division in [7]. Via this approximation, the players determine Φ n , which can be used with the CoL game to find the optimal privacy parameter p * n .…”

“…As privacy-preserving mechanisms we consider both suppression (Sup) and differential privacy (DP). For details, please consult [7]. Fig.…”

“…Training with a concerned. The experiment corresponding to the case when both players can apply privacy preservation can be found in [7].…”

Differential Privacy at Risk: Bridging Randomness and Privacy Budget

“…[7,15] propose game theoretic methods that provide the means to evaluate the monetary cost of differential privacy. Pejó et al [36] also propose a game theoretic cost model in the setting of private collaborative learning. Our approach is inspired by the approach in the work of Hsu et al [19].…”