相关论文: Closure Properties for Private Classification and …
We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\Omega\bigl(\log^*(d)\bigr)$ examples. As a corollary it follows that the class of…
We consider the problem of online classification under a privacy constraint. In this setting a learner observes sequentially a stream of labelled examples $(x_t, y_t)$, for $1 \leq t \leq T$, and returns at each iteration $t$ a hypothesis…
We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm. This answers an open question of Alon et al. (STOC 2019) who proved the converse statement (this…
We study closure properties for the Littlestone and threshold dimensions of binary hypothesis classes. Given classes $\mathcal{H}_1, \ldots, \mathcal{H}_k$ of Boolean functions with bounded Littlestone (respectively, threshold) dimension,…
We study the sample complexity of learning threshold functions under the constraint of differential privacy. It is assumed that each labeled example in the training data is the information of one individual and we would like to come up with…
We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private…
We consider online and PAC learning of Littlestone classes subject to the constraint of approximate differential privacy. Our main result is a private learner to online-learn a Littlestone class with a mistake bound of…
Practical and pervasive needs for robustness and privacy in algorithms have inspired the design of online adversarial and differentially private learning algorithms. The primary quantity that characterizes learnability in these settings is…
The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…
We prove new upper and lower bounds on the sample complexity of $(\epsilon, \delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$…
Alon et al. [2019] and Bun et al. [2020] recently showed that online learnability and private PAC learnability are equivalent in binary classification. We investigate whether this equivalence extends to multi-class classification and…
We show a generic reduction from multiclass differentially private PAC learning to binary private PAC learning. We apply this transformation to a recently proposed binary private PAC learner to obtain a private multiclass learner with…
This work continues to investigate the link between differentially private (DP) and online learning. Alon, Livni, Malliaris, and Moran (2019) showed that for binary concept classes, DP learnability of a given class implies that it has a…
A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008].…
We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of…
In this paper we prove that the sample complexity of properly learning a class of Littlestone dimension $d$ with approximate differential privacy is $\tilde O(d^6)$, ignoring privacy and accuracy parameters. This result answers a question…
In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an…
We initiate a study of computable online (c-online) learning, which we analyze under varying requirements for "optimality" in terms of the mistake bound. Our main contribution is to give a necessary and sufficient condition for optimal…
In 2008, Kasiviswanathan et al. defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while…
A recent line of work has shown a qualitative equivalence between differentially private PAC learning and online learning: A concept class is privately learnable if and only if it is online learnable with a finite mistake bound. However,…