The Role of Adaptive Optimizers for Honest Private Hyperparameter Selection

TL;DR

This paper investigates hyperparameter selection under differential privacy constraints, highlighting the advantages of adaptive optimizers like DPAdam and introducing a new optimizer based on Adam's limiting behavior.

Contribution

It introduces a novel hyperparameter tuning framework for DP machine learning, demonstrating the benefits of adaptive optimizers and providing theoretical insights into their performance.

Findings

Standard composition tools outperform advanced techniques in many DP settings.

An intrinsic connection exists between learning rate and clipping norm hyperparameters.

Adaptive optimizers like DPAdam significantly improve honest hyperparameter tuning.

Abstract

Hyperparameter optimization is a ubiquitous challenge in machine learning, and the performance of a trained model depends crucially upon their effective selection. While a rich set of tools exist for this purpose, there are currently no practical hyperparameter selection methods under the constraint of differential privacy (DP). We study honest hyperparameter selection for differentially private machine learning, in which the process of hyperparameter tuning is accounted for in the overall privacy budget. To this end, we i) show that standard composition tools outperform more advanced techniques in many settings, ii) empirically and theoretically demonstrate an intrinsic connection between the learning rate and clipping norm hyperparameters, iii) show that adaptive optimizers like DPAdam enjoy a significant advantage in the process of honest hyperparameter tuning, and iv) draw upon novel limiting behaviour of Adam in the DP setting to design a new and more efficient optimizer.