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Privacy concern has been increasingly important in many machine learning (ML)problems. We study empirical risk minimization (ERM) problems under securemulti-party computation (MPC) frameworks. Main technical tools for MPC havebeen developed based on cryptography. One of limitations in currentcryptographically private ML is that it is computationally intractable toevaluate non-linear functions such as logarithmic functions or exponentialfunctions. Therefore, for a class of ERM problems such as logistic regressionin which non-linear function evaluations are required, one can only obtainapproximate solutions. In this paper, we introduce a novel cryptographicallyprivate tool called secure approximation guarantee (SAG) method. The keyproperty of SAG method is that, given an arbitrary approximate solution, it canprovide a non-probabilistic assumption-free bound on the approximation qualityunder cryptographically secure computation framework. We demonstrate thebenefit of the SAG method by applying it to several problems including apractical privacy-preserving data analysis task on genomic and clinicalinformation.

Secure Approximation Guarantee for Cryptographically Private Empirical Risk Minimization