Privacy for free in the overparameterized regime.

Area of Science:

• Machine Learning
• Deep Learning
• Privacy-Preserving Technologies

Background:

• Differentially private gradient descent (DP-GD) is crucial for training deep learning models while protecting data privacy.
• Existing research has established upper bounds on the performance cost of DP-GD compared to standard gradient descent (GD).
• These bounds often worsen in overparameterized regimes, common in deep learning, creating uncertainty for practitioners.

Purpose of the Study:

• To investigate the performance cost of DP-GD in overparameterized deep learning models.
• To challenge the conventional understanding that overparameterization inherently degrades privacy-preserving learning performance.
• To provide theoretical insights for practitioners navigating DP-GD in large-scale models.

Main Methods:

• Analysis within the random features model with quadratic loss.
• Theoretical examination of DP-GD performance under varying privacy parameters.
• Investigating the impact of overparameterization (large number of parameters relative to samples) on DP-GD.

Main Results:

• Demonstrated that for sufficiently large models, privacy can be achieved with no excess population risk ([Formula: see text]).
• This finding holds true even for constant-order privacy parameters ([Formula: see text]) and in the strongly private setting ([Formula: see text]).
• The results indicate that overparameterization does not necessarily hinder performance in differentially private learning.

Conclusions:

• Overparameterization in deep learning does not inherently impose a performance penalty when using DP-GD.
• Privacy can be obtained 'for free' in certain overparameterized scenarios, contrary to common assumptions.
• This work offers new theoretical guidance, suggesting that large models can be compatible with strong privacy guarantees.