Katrina Ligett

A learning theory approach to non-interactive database privacy

We demonstrate that, ignoring computational constraints, it is possible to release privacy-preserving databases that are useful for all queries over a discretized domain from any given concept class with polynomial VC-dimension. We show a new lower bound for releasing databases that are useful for halfspace queries over a continuous domain. Despite this, we give a privacy-preserving polynomial time algorithm that releases information useful for all halfspace queries, for a slightly relaxed definition of usefulness. Inspired by learning theory, we introduce a new notion of data privacy, which we call distributional privacy, and show that it is strictly stronger than the prevailing privacy notion, differential privacy.

A learning theory approach to noninteractive database privacy

In this article, we demonstrate that, ignoring computational constraints, it is possible to release synthetic databases that are useful for accurately answering large classes of queries while preserving differential privacy. Specifically, we give a mechanism that privately releases synthetic data useful for answering a class of queries over a discrete domain with error that grows as a function of the size of the smallest net approximately representing the answers to that class of queries. We show that this in particular implies a mechanism for counting queries that gives error guarantees that grow only with the VC-dimension of the class of queries, which itself grows at most logarithmically with the size of the query class. We also show that it is not possible to release even simple classes of queries (such as intervals and their generalizations) over continuous domains with worst-case utility guarantees while preserving differential privacy. In response to this, we consider a relaxation of the utility guarantee and give a privacy preserving polynomial time algorithm that for any halfspace query will provide an answer that is accurate for some small perturbation of the query. This algorithm does not release synthetic data, but instead another data structure capable of representing an answer for each query. We also give an efficient algorithm for releasing synthetic data for the class of interval queries and axis-aligned rectangles of constant dimension over discrete domains.

Take it or leave it: running a survey when privacy comes at a cost

In this paper, we consider the problem of estimating a potentially sensitive (individually stigmatizing) statistic on a population. In our model, individuals are concerned about their privacy, and experience some cost as a function of their privacy loss. Nevertheless, they would be willing to participate in the survey if they were compensated for their privacy cost. These cost functions are not publicly known, however, nor do we make Bayesian assumptions about their form or distribution. Individuals are rational and will misreport their costs for privacy if doing so is in their best interest. Ghosh and Roth recently showed in this setting, when costs for privacy loss may be correlated with private types, if individuals value differential privacy, no individually rational direct revelation mechanism can compute any non-trivial estimate of the population statistic. In this paper, we circumvent this impossibility result by proposing a modified notion of how individuals experience cost as a function of their privacy loss, and by giving a mechanism which does not operate by direct revelation. Instead, our mechanism has the ability to randomly approach individuals from a population and offer them a take-it-or-leave-it offer. This is intended to model the abilities of a surveyor who may stand on a street corner and approach passers-by.

On the price of stability for undirected network design

We continue the study of the effects of selfish behavior in the network design problem. We provide new bounds for the price of stability for network design with fair cost allocation for undirected graphs. We consider the most general case, for which the best known upper bound is the Harmonic number Hn, where n is the number of agents, and the best previously known lower bound is 12/7≈1.778. We present a nontrivial lower bound of 42/23≈1.8261. Furthermore, we show that for two players, the price of stability is exactly 4/3, while for three players it is at least 74/48≈1.542 and at most 1.65. These are the first improvements on the bound of Hn for general networks. In particular, this demonstrates a separation between the price of stability on undirected graphs and that on directed graphs, where Hn is tight. Previously, such a gap was only known for the cases where all players have a shared source, and for weighted players.

A tale of two metrics: simultaneous bounds on competitiveness and regret

We consider algorithms for “smoothed online convex optimization” (SOCO) problems, which are a hybrid between online convex optimization (OCO) and metrical task system (MTS) problems. Historically, the performance metric for OCO was regret and that for MTS was competitive ratio (CR). There are algorithms with either sublinear regret or constant CR, but no known algorithm achieves both simultaneously. We show that this is a fundamental limitation – no algorithm (deterministic or randomized) can achieve sublinear regret and a constant CR, even when the objective functions are linear and the decision space is one dimensional. However, we present an algorithm that, for the important one dimensional case, provides sublinear regret and a CR that grows arbitrarily slowly.

Differential privacy with compression

This work studies formal utility and privacy guarantees for a simple multiplicative database transformation, where the data are compressed by a random linear or affine transformation, reducing the number of data records substantially, while preserving the number of original input variables.We provide an analysis framework inspired by a recent concept known as differential privacy. Our goal is to show that, despite the general difficulty of achieving the differential privacy guarantee, it is possible to publish synthetic data that are useful for a number of common statistical learning applications. This includes high dimensional sparse regression [24], principal component analysis (PCA), and other statistical measures [16] based on the covariance of the initial data.

Improved bounds on the price of stability in network cost sharing games

We study the price of stability in undirected network design games with fair cost sharing. Our work provides multiple new pieces of evidence that the true price of stability, at least for special subclasses of games, may be a constant. We make progress on this long-outstanding problem, giving a bound of O(log log log n) on the price of stability of undirected broadcast games (where n is the number of players). This is the first progress on the upper bound for this problem since the O(log log n) bound of [Fiat et al. 2006](despite much attention, the known lower bound remains at 1.818, from [Bilò et al. 2010. Our proofs introduce several new techniques that may be useful in future work. We provide further support for the conjectured constant price of stability in the form of a comprehensive analysis of an alternative solution concept that forces deviating players to bear the entire costs of building alternative paths. This solution concept includes all Nash equilibria and can be viewed as a relaxation thereof, but we show that it preserves many properties of Nash equilibria. We prove that the price of stability in multicast games for this relaxed solution concept is Θ(1), which may suggest that similar results should hold for Nash equilibria. This result also demonstrates that the existing techniques for lower bounds on the Nash price of stability in undirected network design games cannot be extended to be super-constant, as our relaxation concept encompasses all equilibria constructed in them.

Accuracy for Sale: Aggregating Data with a Variance Constraint

We consider the problem of a data analyst who may purchase an unbiased estimate of some statistic from multiple data providers. From each provider i, the analyst has a choice: she may purchase an estimate from that provider that has variance chosen from a finite menu of options. Each level of variance has a cost associated with it, reported (possibly strategically) by the data provider. The analyst wants to choose the minimum cost set of variance levels, one from each provider, that will let her combine her purchased estimators into an aggregate estimator that has variance at most some fixed desired level. Moreover, she wants to do so in such a way that incentivizes the data providers to truthfully report their costs to the mechanism. We give a dominant strategy truthful solution to this problem that yields an estimator that has optimal expected cost, and violates the variance constraint by at most an additive term that tends to zero as the number of data providers grows large.

Playing Games with Approximation Algorithms

In an online linear optimization problem, on each period

Beating the best Nash without regret

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