arXiv subjects

Aaron Roth

Publications and source records attributed to Aaron Roth.

At least 145 records · Page 8Linked to original sources

arXiv2015

Privacy for the Protected (Only)

Motivated by tensions between data privacy for individual citizens, and societal priorities such as counterterrorism and the containment of infectious disease, we introduce a computational model that distinguishes between parties for whom privacy is explicitly protected, and those for whom it is not (the targeted subpopulation). The goal is the development of algorithms that can effectively identify and take action upon members of the targeted subpopulation in a way that minimally compromises the privacy of the protected, while simultaneously limiting the expense of distinguishing members of the two groups via costly mechanisms such as surveillance, background checks, or medical testing. Within this framework, we provide provably privacy-preserving algorithms for targeted search in social networks. These algorithms are natural variants of common graph search methods, and ensure privacy for the protected by the careful injection of noise in the prioritization of potential targets. We validate the utility of our algorithms with extensive computational experiments on two large-scale social network datasets.

cs.DS↗

arXiv2015

Inducing Approximately Optimal Flow Using Truthful Mediators

We revisit a classic coordination problem from the perspective of mechanism design: how can we coordinate a social welfare maximizing flow in a network congestion game with selfish players? The classical approach, which computes tolls as a function of known demands, fails when the demands are unknown to the mechanism designer, and naively eliciting them does not necessarily yield a truthful mechanism. Instead, we introduce a weak mediator that can provide suggested routes to players and set tolls as a function of reported demands. However, players can choose to ignore or misreport their type to this mediator. Using techniques from differential privacy, we show how to design a weak mediator such that it is an asymptotic ex-post Nash equilibrium for all players to truthfully report their types to the mediator and faithfully follow its suggestion, and that when they do, they end up playing a nearly optimal flow. Notably, our solution works in settings of incomplete information even in the absence of a prior distribution on player types. Along the way, we develop new techniques for privately solving convex programs which may be of independent interest.

cs.GT↗

arXiv2015

Privacy and Truthful Equilibrium Selection for Aggregative Games

We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players $n$. We also apply our main results to a multi-dimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games -- previously, they were only known to exist in traffic routing games.

cs.DS↗

arXiv2015

Private Pareto Optimal Exchange

We consider the problem of implementing an individually rational, asymptotically Pareto optimal allocation in a barter-exchange economy where agents are endowed with goods and have preferences over the goods of others, but may not use money as a medium of exchange. Because one of the most important instantiations of such economies is kidney exchange -- where the "input"to the problem consists of sensitive patient medical records -- we ask to what extent such exchanges can be carried out while providing formal privacy guarantees to the participants. We show that individually rational allocations cannot achieve any non-trivial approximation to Pareto optimality if carried out under the constraint of differential privacy -- or even the relaxation of \emph{joint} differential privacy, under which it is known that asymptotically optimal allocations can be computed in two-sided markets, where there is a distinction between buyers and sellers and we are concerned only with privacy of the buyers~\citep{Matching}. We therefore consider a further relaxation that we call \emph{marginal} differential privacy -- which promises, informally, that the privacy of every agent $i$ is protected from every other agent $j \neq i$ so long as $j$ does not collude or share allocation information with other agents. We show that, under marginal differential privacy, it is possible to compute an individually rational and asymptotically Pareto optimal allocation in such exchange economies.

cs.GT↗

arXiv2014

Online Learning and Profit Maximization from Revealed Preferences

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also consider an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings.

cs.DS↗

arXiv2014

Distributed Private Heavy Hitters

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the $n$ parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large.

cs.DS↗

arXiv2014

Jointly Private Convex Programming

In this paper we present an extremely general method for approximately solving a large family of convex programs where the solution can be divided between different agents, subject to joint differential privacy. This class includes multi-commodity flow problems, general allocation problems, and multi-dimensional knapsack problems, among other examples. The accuracy of our algorithm depends on the \emph{number} of constraints that bind between individuals, but crucially, is \emph{nearly independent} of the number of primal variables and hence the number of agents who make up the problem. As the number of agents in a problem grows, the error we introduce often becomes negligible. We also consider the setting where agents are strategic and have preferences over their part of the solution. For any convex program in this class that maximizes \emph{social welfare}, there is a generic reduction that makes the corresponding optimization \emph{approximately dominant strategy truthful} by charging agents prices for resources as a function of the approximately optimal dual variables, which are themselves computed under differential privacy. Our results substantially expand the class of problems that are known to be solvable under both privacy and incentive constraints.

cs.DS↗

arXiv2014

Higher-Order Approximate Relational Refinement Types for Mechanism Design and Differential Privacy

Mechanism design is the study of algorithm design in which the inputs to the algorithm are controlled by strategic agents, who must be incentivized to faithfully report them. Unlike typical programmatic properties, it is not sufficient for algorithms to merely satisfy the property---incentive properties are only useful if the strategic agents also believe this fact. Verification is an attractive way to convince agents that the incentive properties actually hold, but mechanism design poses several unique challenges: interesting properties can be sophisticated relational properties of probabilistic computations involving expected values, and mechanisms may rely on other probabilistic properties, like differential privacy, to achieve their goals. We introduce a relational refinement type system, called $\mathsf{HOARe}^2$, for verifying mechanism design and differential privacy. We show that $\mathsf{HOARe}^2$ is sound w.r.t. a denotational semantics, and correctly models $(ε,δ)$-differential privacy; moreover, we show that it subsumes DFuzz, an existing linear dependent type system for differential privacy. Finally, we develop an SMT-based implementation of $\mathsf{HOARe}^2$ and use it to verify challenging examples of mechanism design, including auctions and aggregative games, and new proposed examples from differential privacy.

cs.PL↗

arXiv2014

Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets.

cs.GT↗

arXiv2014

An Anti-Folk Theorem for Large Repeated Games with Imperfect Monitoring

We study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems that show that when the signals observed by the players satisfy a condition known as $(ε, γ)$-differential privacy, that the folk theorem has little bite: for values of $ε$ and $γ$ sufficiently small, for a fixed discount factor, any equilibrium of the repeated game involve players playing approximate equilibria of the stage game in every period. Next, we argue that in large games ($n$ player games in which unilateral deviations by single players have only a small impact on the utility of other players), many monitoring settings naturally lead to signals that satisfy $(ε,γ)$-differential privacy, for $ε$ and $γ$ tending to zero as the number of players $n$ grows large. We conclude that in such settings, the set of equilibria of the repeated game collapse to the set of equilibria of the stage game.

cs.GT↗

arXiv2014

Privately Solving Linear Programs

In this paper, we initiate the systematic study of solving linear programs under differential privacy. The first step is simply to define the problem: to this end, we introduce several natural classes of private linear programs that capture different ways sensitive data can be incorporated into a linear program. For each class of linear programs we give an efficient, differentially private solver based on the multiplicative weights framework, or we give an impossibility result.

cs.DS↗

arXiv2014

Buying Private Data without Verification

We consider the problem of designing a survey to aggregate non-verifiable information from a privacy-sensitive population: an analyst wants to compute some aggregate statistic from the private bits held by each member of a population, but cannot verify the correctness of the bits reported by participants in his survey. Individuals in the population are strategic agents with a cost for privacy, \ie, they not only account for the payments they expect to receive from the mechanism, but also their privacy costs from any information revealed about them by the mechanism's outcome---the computed statistic as well as the payments---to determine their utilities. How can the analyst design payments to obtain an accurate estimate of the population statistic when individuals strategically decide both whether to participate and whether to truthfully report their sensitive information? We design a differentially private peer-prediction mechanism that supports accurate estimation of the population statistic as a Bayes-Nash equilibrium in settings where agents have explicit preferences for privacy. The mechanism requires knowledge of the marginal prior distribution on bits $b_i$, but does not need full knowledge of the marginal distribution on the costs $c_i$, instead requiring only an approximate upper bound. Our mechanism guarantees $ε$-differential privacy to each agent $i$ against any adversary who can observe the statistical estimate output by the mechanism, as well as the payments made to the $n-1$ other agents $j\neq i$. Finally, we show that with slightly more structured assumptions on the privacy cost functions of each agent, the cost of running the survey goes to $0$ as the number of agents diverges.

cs.GT↗

arXiv2014

Differential Privacy: An Economic Method for Choosing Epsilon

Differential privacy is becoming a gold standard for privacy research; it offers a guaranteed bound on loss of privacy due to release of query results, even under worst-case assumptions. The theory of differential privacy is an active research area, and there are now differentially private algorithms for a wide range of interesting problems. However, the question of when differential privacy works in practice has received relatively little attention. In particular, there is still no rigorous method for choosing the key parameter $ε$, which controls the crucial tradeoff between the strength of the privacy guarantee and the accuracy of the published results. In this paper, we examine the role that these parameters play in concrete applications, identifying the key questions that must be addressed when choosing specific values. This choice requires balancing the interests of two different parties: the data analyst and the prospective participant, who must decide whether to allow their data to be included in the analysis. We propose a simple model that expresses this balance as formulas over a handful of parameters, and we use our model to choose $ε$ on a series of simple statistical studies. We also explore a surprising insight: in some circumstances, a differentially private study can be more accurate than a non-private study for the same cost, under our model. Finally, we discuss the simplifying assumptions in our model and outline a research agenda for possible refinements.

cs.DB↗

arXiv2014

Constrained Signaling in Auction Design

We consider the problem of an auctioneer who faces the task of selling a good (drawn from a known distribution) to a set of buyers, when the auctioneer does not have the capacity to describe to the buyers the exact identity of the good that he is selling. Instead, he must come up with a constrained signalling scheme: a (non injective) mapping from goods to signals, that satisfies the constraints of his setting. For example, the auctioneer may be able to communicate only a bounded length message for each good, or he might be legally constrained in how he can advertise the item being sold. Each candidate signaling scheme induces an incomplete-information game among the buyers, and the goal of the auctioneer is to choose the signaling scheme and accompanying auction format that optimizes welfare. In this paper, we use techniques from submodular function maximization and no-regret learning to give algorithms for computing constrained signaling schemes for a variety of constrained signaling problems.

cs.GT↗

arXiv2013

Privacy and Mechanism Design

This paper is a survey of recent work at the intersection of mechanism design and privacy. The connection is a natural one, but its study has been jump-started in recent years by the advent of differential privacy, which provides a rigorous, quantitative way of reasoning about the costs that an agent might experience because of the loss of his privacy. Here, we survey several facets of this study, and differential privacy plays a role in more than one way. Of course, it provides us a basis for modeling agent costs for privacy, which is essential if we are to attempt mechanism design in a setting in which agents have preferences for privacy. It also provides a toolkit for controlling those costs. However, perhaps more surprisingly, it provides a powerful toolkit for controlling the stability of mechanisms in general, which yields a set of tools for designing novel mechanisms even in economic settings completely unrelated to privacy.

cs.GT↗

arXiv2013

Differential Privacy for the Analyst via Private Equilibrium Computation

We give new mechanisms for answering exponentially many queries from multiple analysts on a private database, while protecting differential privacy both for the individuals in the database and for the analysts. That is, our mechanism's answer to each query is nearly insensitive to changes in the queries asked by other analysts. Our mechanism is the first to offer differential privacy on the joint distribution over analysts' answers, providing privacy for data analysts even if the other data analysts collude or register multiple accounts. In some settings, we are able to achieve nearly optimal error rates (even compared to mechanisms which do not offer analyst privacy), and we are able to extend our techniques to handle non-linear queries. Our analysis is based on a novel view of the private query-release problem as a two-player zero-sum game, which may be of independent interest.

cs.DS↗

arXiv2012

Exploiting Metric Structure for Efficient Private Query Release

We consider the problem of privately answering queries defined on databases which are collections of points belonging to some metric space. We give simple, computationally efficient algorithms for answering distance queries defined over an arbitrary metric. Distance queries are specified by points in the metric space, and ask for the average distance from the query point to the points contained in the database, according to the specified metric. Our algorithms run efficiently in the database size and the dimension of the space, and operate in both the online query release setting, and the offline setting in which they must in polynomial time generate a fixed data structure which can answer all queries of interest. This represents one of the first subclasses of linear queries for which efficient algorithms are known for the private query release problem, circumventing known hardness results for generic linear queries.

cs.DS↗

arXiv2012

Efficiently Learning from Revealed Preference

In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some unknown utility function, subject to the given prices and budget constraint. We wish not only to find a utility function which rationalizes a finite set of observations, but to produce a hypothesis valuation function which accurately predicts the behavior of the agent in the future. We give efficient algorithms with polynomial sample-complexity for agents with linear valuation functions, as well as for agents with linearly separable, concave valuation functions with bounded second derivative.

cs.GT↗