[Paper Review] The Differentially Private Lottery Ticket Mechanism

Lovedeep Gondara, Ke Wang+1 more|arXiv (Cornell University)|Feb 16, 2020

Gambling Behavior and Treatments20 references4 citations

TL;DR

The paper proposes the Differentially Private Lottery Ticket Mechanism (DPLTM), an end-to-end differentially private training framework that leverages the lottery ticket hypothesis to identify high-quality, sparse subnetworks (winning tickets) via a custom score function. DPLTM achieves superior privacy-utility trade-offs over DPSGD, converges faster, enables early stopping with reduced privacy budget, and demonstrates transferability of winning tickets across datasets, domains, and architectures.

ABSTRACT

We propose the differentially private lottery ticket mechanism (DPLTM). An end-to-end differentially private training paradigm based on the lottery ticket hypothesis. Using "high-quality winners", selected via our custom score function, DPLTM significantly improves the privacy-utility trade-off over the state-of-the-art. We show that DPLTM converges faster, allowing for early stopping with reduced privacy budget consumption. We further show that the tickets from DPLTM are transferable across datasets, domains, and architectures. Our extensive evaluation on several public datasets provides evidence to our claims.

Motivation & Objective

• Address the privacy-utility trade-off bottleneck in differentially private deep learning, where large model sizes amplify noise, degrading utility.
• Extend the lottery ticket hypothesis to end-to-end differentially private training, ensuring privacy throughout ticket selection and training.
• Develop a custom score function to identify high-utility, low-parameter winning tickets that improve privacy-utility balance.
• Demonstrate transferability of winning tickets across datasets, domains, and architectures to reduce privacy costs in downstream tasks.
• Achieve state-of-the-art performance across multiple datasets under tight privacy budgets (e.g., ε = 0.2), outperforming DPSGD.

Proposed method

• Phase 1: Generate lottery tickets by pruning a randomly initialized large neural network using magnitude-based pruning.
• Phase 2: Select the winning ticket using the Exponential Mechanism with a custom score function that prioritizes high utility and low parameter count.
• The score function balances model performance and sparsity, ensuring the selected ticket is both accurate and lightweight.
• Phase 3: Train the selected winning ticket using differentially private stochastic gradient descent (DPSGD), with gradient clipping and noise injection.
• Apply differential privacy to all stages: ticket generation, selection, and training, ensuring end-to-end (ε, δ)-differential privacy.
• Use the Exponential Mechanism’s probability distribution to select tickets with utility-proportional likelihood, ensuring privacy during selection.

Experimental results

Research questions

• RQ1 Can the lottery ticket hypothesis be extended to end-to-end differentially private deep learning while preserving privacy guarantees?
• RQ2 Does selecting winning tickets via a custom score function improve the privacy-utility trade-off compared to random or heuristic selection?
• RQ3 Can DPLTM achieve faster convergence than DPSGD, enabling earlier stopping and reduced privacy budget consumption?
• RQ4 Are winning tickets from DPLTM transferable across different datasets, domains, and model architectures?
• RQ5 How does DPLTM perform under tight privacy budgets (e.g., ε = 0.2) compared to state-of-the-art DPSGD?

Key findings

• DPLTM significantly outperforms DPSGD across all five evaluated datasets (MNIST, HAR, Fashion-MNIST, Kuzushiji-MNIST, ISOLET) under all privacy budgets.
• At ε = 0.2, DPLTM achieves 84% accuracy on MNIST, compared to 79% with a randomly selected ticket, demonstrating the efficacy of the score function.
• DPLTM converges faster than DPSGD, enabling earlier stopping and reducing privacy budget consumption while maintaining or improving utility.
• Winning tickets from DPLTM are transferable across datasets and architectures, enabling lower-privacy-cost training on new tasks.
• The performance gap between DPLTM and DPSGD widens as privacy becomes tighter (e.g., ε = 0.2), confirming improved privacy-utility trade-offs.
• The custom score function effectively identifies high-utility, low-parameter tickets, as evidenced by consistent performance gains over random selection.