Renyi Differentially Private ADMM for Non-Smooth Regularized Optimization
This work addresses privacy-preserving optimization for machine learning tasks, offering incremental improvements in performance under strict privacy constraints.
The paper tackles the problem of minimizing composite objective functions with non-smooth regularization under Rényi differential privacy by proposing two stochastic ADMM algorithms, ssADMM and mpADMM, which outperform baseline methods in high privacy regimes for classification and feature selection tasks.
In this paper we consider the problem of minimizing composite objective functions consisting of a convex differentiable loss function plus a non-smooth regularization term, such as $L_1$ norm or nuclear norm, under Rényi differential privacy (RDP). To solve the problem, we propose two stochastic alternating direction method of multipliers (ADMM) algorithms: ssADMM based on gradient perturbation and mpADMM based on output perturbation. Both algorithms decompose the original problem into sub-problems that have closed-form solutions. The first algorithm, ssADMM, applies the recent privacy amplification result for RDP to reduce the amount of noise to add. The second algorithm, mpADMM, numerically computes the sensitivity of ADMM variable updates and releases the updated parameter vector at the end of each epoch. We compare the performance of our algorithms with several baseline algorithms on both real and simulated datasets. Experimental results show that, in high privacy regimes (small $ε$), ssADMM and mpADMM outperform other baseline algorithms in terms of classification and feature selection performance, respectively.