DP-ADMM: ADMM-based Distributed Learning with Differential Privacy (1808.10101v6)

Abstract: Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

• The paper introduces DP-ADMM, a novel algorithm that integrates differential privacy with the ADMM framework for distributed learning, even under non-smooth objectives.
• It employs adaptive Gaussian noise and time-varying step sizes to maintain strong privacy guarantees while achieving an O(1/√t) convergence rate.
• Experimental results demonstrate improved efficiency and accuracy over standard ADMM and differentially private SGD on real-world logistic regression tasks.

Overview of "DP-ADMM: ADMM-based Distributed Learning with Differential Privacy"

Introduction

The paper introduces a novel algorithm, DP-ADMM, addressing privacy concerns in distributed machine learning setups. The core of the research revolves around enhancing the Alternating Direction Method of Multipliers (ADMM) with differential privacy guarantees, applicable even to non-smooth and non-strongly convex objective functions. This contribution is significant in distributed learning environments where data privacy is pivotal, necessitating robust mechanisms for privacy preservation without sacrificing model utility.

Methodology

DP-ADMM innovatively modifies the standard ADMM framework by incorporating an approximate augmented Lagrangian function combined with adaptive Gaussian noise injection. This approximation replaces exact computation with a more computationally efficient approach, providing closed-form solutions even in non-smooth cases. This is a critical advancement, as previous approaches to privacy-preserving ADMM lagged in efficacy under stringent privacy guarantees and were limited to strongly convex objectives.

Central to the utility of DP-ADMM is its preservation across varying types of distributed learning scenarios through two adaptations: the use of time-varying step sizes and Gaussian noise magnitudes. The time-varying aspect ensures that the algorithm remains efficient across iterations, gradually reducing variance to stabilize the learning process while maintaining privacy protection.

Privacy and Convergence Analysis

The privacy analysis of DP-ADMM utilizes the moments accountant method, a sophisticated technique for evaluating cumulative privacy loss over iterative processes, establishing that DP-ADMM can achieve strong end-to-end privacy guarantees. The privacy is parameterized by $(\epsilon, \delta)$-differential privacy definitions, ensuring robustness even throughout substantial iterative cycles.

From a convergence perspective, DP-ADMM demonstrates promising theoretical properties, with formal convergence rates established for both smooth and non-smooth cases. Notably, the algorithm achieves an $O(1/\sqrt{t})$ convergence rate, aligning with competitive expectations in distributed optimization and ensuring reliable performance across model updates. The explicit trade-off between privacy budget limitations and model utility is clear, providing a structured understanding for researchers.

Experimental Evaluation

Extensive simulations validate the theoretical robustness of DP-ADMM, exhibiting solid performance on real-world datasets with a focus on logistic regression tasks. The simulation results demonstrate superior utility, accuracy, and computational efficiency of DP-ADMM compared to existing baseline algorithms including standard ADMM with perturbation and differentially private stochastic gradient descent.

Implications and Future Research Directions

The practical implications of DP-ADMM extend beyond mere algorithmic improvement. By enabling privacy-preserving distributed learning over datasets that could be sensitive, DP-ADMM supports a range of potential applications in scenarios where data disclosure is restricted. The advancements in differential privacy further bolster confidence in employing distributed machine learning in privacy-constrained environments.

Future research could advance this groundwork by exploring extensions to non-convex settings or hybrid models incorporating federated learning paradigms. Additionally, balancing privacy with efficiency for large-scale systems remains a rich area of investigation. These advancements should continue to focus on computational aspects and privacy dynamics, ensuring scalable and secure adoption in distributed AI systems.

In conclusion, this paper represents a pivotal step in solving privacy challenges in distributed machine learning, presenting an algorithm that harmonizes differential privacy with utility, thereby addressing fundamental concerns in the domain.