Proactive DP: A Multple Target Optimization Framework for DP-SGD
Marten van Dijk, Nhuong V. Nguyen, Toan N. Nguyen, Lam M. Nguyen, Phuong Ha Nguyen
TL;DR
The paper introduces proactive DP, a multi-target optimization framework for DP-SGD that enables a priori selection of hyperparameters under a fixed privacy budget to maximize utility. It combines a tight closed-form DP guarantee $\sigma = \sqrt{2(\epsilon+\ln(1/\delta))/\epsilon}$ with a utility graph and a DP-calculator to jointly optimize privacy and accuracy, and it proves near-tightness of the derived bounds via an explicit lower bound on the number of rounds $T$. A refined, non-asymptotic moment accountant yields practical theorems (Theorem \ref{thm1}, Theorem \ref{thm:simpleF}) that connect sampling, rounds, and noise to DP guarantees, and an implementation flow is provided to guide parameter selection in practice. Extensive experiments across strongly convex, plain convex, and non-convex tasks demonstrate that proactive DP can achieve small $\epsilon$ budgets (e.g., $\epsilon \approx 0.05$–$0.15$) with limited accuracy loss, validating the approach’s effectiveness for privacy-preserving distributed learning.
Abstract
We introduce a multiple target optimization framework for DP-SGD referred to as pro-active DP. In contrast to traditional DP accountants, which are used to track the expenditure of privacy budgets, the pro-active DP scheme allows one to a-priori select parameters of DP-SGD based on a fixed privacy budget (in terms of $ε$ and $δ$) in such a way to optimize the anticipated utility (test accuracy) the most. To achieve this objective, we first propose significant improvements to the moment account method, presenting a closed-form $(ε,δ)$-DP guarantee that connects all parameters in the DP-SGD setup. We show that DP-SGD is $(ε<0.5,δ=1/N)$-DP if $σ=\sqrt{2(ε+\ln(1/δ))/ε}$ with $T$ at least $\approx 2k^2/ε$ and $(2/e)^2k^2-1/2\geq \ln(N)$, where $T$ is the total number of rounds, and $K=kN$ is the total number of gradient computations where $k$ measures $K$ in number of epochs of size $N$ of the local data set. We prove that our expression is close to tight in that if $T$ is more than a constant factor $\approx 4$ smaller than the lower bound $\approx 2k^2/ε$, then the $(ε,δ)$-DP guarantee is violated. The above DP guarantee can be enhanced in thatDP-SGD is $(ε, δ)$-DP if $σ= \sqrt{2(ε+\ln(1/δ))/ε}$ with $T$ at least $\approx 2k^2/ε$ together with two additional, less intuitive, conditions that allow larger $ε\geq 0.5$. Our DP theory allows us to create a utility graph and DP calculator. These tools link privacy and utility objectives and search for optimal experiment setups, efficiently taking into account both accuracy and privacy objectives, as well as implementation goals. We furnish a comprehensive implementation flow of our proactive DP, with rigorous experiments to showcase the proof-of-concept.