Private learning improves sample efficiency for component based models
Private Component-by-Component Learning
Machine LearningCryptography and Security
Summary
This paper tackles how to build private learning models composed of multiple parts while keeping data privacy. The authors solve a problem where small mistakes in learning each part can ruin the overall model’s accuracy. They use a technique called LabelBoost to fix these problems and recycle data efficiently. Their approach reduces the amount of private data needed to learn models with many parts, improving over earlier methods. They also show their methods work well for learning geometric shapes and combinations of simpler models.
What this means in practice
- •For machine learning engineers: Train complex models made of many parts with less private data needed, improving data efficiency under privacy constraints.
- •For data privacy teams: Implement private learning algorithms that scale better with the number of components, reducing privacy costs in multi-part model training.
A theory result. No direct application yet.
Authors
Dvir Karni, Eliad Tsfadia
Abstract
We study differentially private learning problems in the realizable setting, where a hypothesis is specified by $k$ components. A direct iteration of private component learners is obstructed by a simple difficulty: an approximate choice of the next component may destroy exact realizability of the labeled sample, even when the next component is locally accurate. We restore realizability using the LabelBoost procedure of Beimel, Nissim, and Stemmer [SODA '15, Algorithmica '21] and recycle data through two alternating reservoirs. The resulting learner, for a target privacy $\varepsilon$, pays only $\widetilde O(\sqrt{k}/\varepsilon)$ overhead relative to the active sample requirement of a single component learning step at target accuracy $Θ(α/k)$. For learning $d$-dimensional halfspaces over a finite coordinate grid of size $L$, exact realizability makes the direct component-depth objective quasi-concave. Instantiating the framework with the IPConcave algorithm of Nissim, Tsfadia, and Yan [SODA '26] and with the quasi-concave optimizer of Cohen, Lyu, Nelson, Sarl'os, and Stemmer [STOC '23] yields a realizable sample complexity of $\widetilde{O}\left(\frac{1}{\varepsilon α}\cdot \min\{d^{2.5} \log^*L, \:\: d^{2.5} + d^{1.5} 2^{\log^*L}\}\right),$ which improves on the previously known bound of $\widetilde{O}\left(\frac{1}{\varepsilon α}\cdot\min\{\frac{1}α\cdot d^{5.5}\log^*L,\:\: d^{2.5}2^{\log^*L}\}\right).$ We also apply the framework to Boolean compositions: given proper private learners for classes $H_1,\ldots,H_k$, we obtain a proper private learner for $G(H_1,\ldots,H_k)$ for any fixed Boolean function $G:\{0,1\}^k\to\{0,1\}$. Compared with the closure theorem of Alon, Beimel, Moran, and Stemmer [COLT '20], this reduces the overhead on a common component sample bound from $\widetilde O(k/\varepsilon)$ to $\widetilde O(\sqrt{k}/\varepsilon)$.