Differentially Private Worst-group Risk Minimization

Authors: Xinyu Zhou, Raef Bassily

ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We initiate a systematic study of worst-group risk minimization under (ϵ, δ)-differential privacy (DP). The goal is to privately find a model that approximately minimizes the maximal risk across p sub-populations (groups) with different distributions, where each group distribution is accessed via a sample oracle. We first present a new algorithm that achieves excess worst-group population risk of O( p d K ), where K is the total number of samples drawn from all groups and d is the problem dimension. Our rate is nearly optimal when each distribution is observed via a fixedsize dataset of size K/p. Our result is based on a new stability-based analysis for the generalization error. In particular, we show that -uniform argument stability implies O( + 1 n) generalization error w.r.t. the worst-group risk, where n is the number of samples drawn from each sample oracle. Next, we propose an algorithmic framework for worst-group population risk minimization using any DP online convex optimization algorithm as a subroutine. Hence, we give another excess risk bound of O q ϵK + p p Kϵ2 + p p Assuming the typical setting of ϵ = Θ(1), this bound is more favorable than our first bound in a certain range of p as a function of K and d. Finally, we study differentially private worst-group empirical risk minimization in the offline setting, where each group distribution is observed by a fixed-size dataset. We present a new algorithm with nearly optimal excess risk of O( p d K ).
Researcher Affiliation Academia 1Department of Computer Science & Engineering, The Ohio State University 2Department of Computer Science & Engineering and the Translational Data Analytics Institute (TDAI), The Ohio State University.
Pseudocode Yes Algorithm 1 Minimax Phased ERM Algorithm 2 Worst-group risk minimization using DP-OCO algorithm Algorithm 3 Noisy SGD with Multiplicative Group Reweighting (Noisy-SGD-MGR) Algorithm 4 Minimax Optimization for SC-SC Objective
Open Source Code No No statement or link to open-source code is provided in the paper.
Open Datasets No The paper is theoretical and describes a model that accesses data via
Dataset Splits No The paper is theoretical and does not describe empirical dataset splits for validation, training, or testing.
Hardware Specification No The paper is theoretical and does not describe any specific hardware used for experiments.
Software Dependencies No The paper is theoretical and does not list specific software dependencies with version numbers for reproducibility of experiments. It references algorithms like DP-FTRL but not specific software environments.
Experiment Setup No The paper is theoretical and does not describe an empirical experimental setup with concrete hyperparameters or training configurations.