Differential Privacy Book is Here

After a much longer time than either of us thought it would take, my book with Cynthia Dwork, "The Algorithmic Foundations of Differential Privacy" is finally available.

You have 3 options for obtaining a copy! (I must admit to not quite understanding the pricing model of our publisher).

1. Hard Copy: You can buy a hard copy directly from NOW for $99 (http://www.nowpublishers.com/articles/foundations-and-trends-in-theoretical-computer-science/TCS-042/book-details) or from Amazon for $101 and free shipping (http://www.amazon.com/Algorithmic-Foundations-Differential-Privacy/dp/1601988184/ )
2. "ebook" format (which I believe is just a downloadable pdf): If you don't have room on your book shelf, and are happy with a PDF, the book can be yours from NOW for only $240. This is a bargain -- coming in at 281 pages, this is less than 86 cents per digital "page".   (http://www.nowpublishers.com/articles/foundations-and-trends-in-theoretical-computer-science/TCS-042/book-details)
3. Free download: The PDF is also available for free on my web page: http://www.cis.upenn.edu/~aaroth/privacybook.html

Lecture 12 -- Privacy Yields an Anti-Folk Theorem in Repeated Games

Last week, Kobbi Nissim gave us an excellent guest lecture on differential privacy and machine learning. The semester has gone by fast -- this week is our last lecture in the privacy and mechanism design class. (But stop by next week to hear the students present their research projects!)

Today we'll talk about infinitely repeated games. In an infinitely repeated game, n players repeatedly, in an infinite number of stages, play actions and obtain payoffs based on some commonly known stage game. Since the game is infinitely repeated, in order to make sense of players total payoff, we employ a discount factor delta that specifies how much less valuable a dollar is tomorrow compared to a dollar today. (delta is some number in [0, 1) ). In games of perfect monitoring, players perfectly observe what actions each of their opponents have played in past rounds, but in large n player games, it is much more natural to think about games of imperfect monitoring, in which agents see only some noisy signal of what their opponents have played.

For example, one natural signal players might observe in an anonymous game is a noisy histogram estimating what fraction of the population has played each type of action. (This is the kind of signal you might get if you see a random subsample of what people play -- for example, you have an estimate of how many people drove on each road on the way to work today by looking at traffic reports). Alternately, there may be some low dimensional signal (like the market price of some good) that everyone observes that is computed as a randomized function of everyone's actions today (e.g. how much of the good each person produced).

A common theme in repeated games of all sorts are folk theorems. Informally, these theorems state that in repeated games, we should expect a huge multiplicity of equilibria, well beyond the equilibria we would see in the corresponding one-shot stage game. This is because players observe each other's past behavior, and so can threaten each other to behave in prescribed ways or else face punishment. Whether or not a folk theorem is a positive result or a negative result depends on whether you want to design behavior, or predict behavior. If you are a mechanism designer, a folk theorem might be good news -- you can try and encourage equilibrium behavior that has higher welfare than any equilibrium of the stage game. However, if you want to predict behavior, it is bad news -- there are now generically a huge multiplicity of very different equilibria, and some of them have much worse welfare than any equilibrium of the stage game.

In this lecture (following a paper joint with Mallesh Pai and Jon Ullman) we argue that:

1. In large games, many natural signaling structures produce signal distributions that are differentially private in the actions of the players, where the privacy parameters tends to 0 as the size of the game gets large, and
2. In any such game, for any discount factor delta, as the size of the game gets large, the set of equilibria of the repeated game collapse to the set of equilibria of the stage game. In other words, there are no "folk theorem equilibria" -- only the equilibria that already existed in the one shot game. 

This could be interpreted in a couple of ways. On the one hand, this means that in large games, it might be harder to sustain cooperation (which is a negative result). On the other hand, since it shrinks the set of equilibria, it means that adding noise to the signaling structure in a large game generically improves the price of anarchy over equilibria of the repeated game, which is a positive result. 

Lecture 10 -- Running Ascending Price Auctions that Make Sincere Bidding an Ex-Post Dominant Strategy

In the 10th lecture in our privacy and mechanism design class, we consider the problem of running an ascending price auction. An ascending price auction is just a generalization of what you normally see as an "auction" on TV -- rather than submitting your valuation in some kind of one-shot protocol, the prices of the goods gradually rise, and you take turns with other bidders making bids on the goods as a function of the current prices.

Why would you want to run such an auction when the VCG mechanism already can provide welfare optimal outcomes for every social choice function, while making truthful reporting a dominant strategy? People quote a couple of reasons:

1. It might be hard to actually report your full valuation: in principle, you need to figure out exactly your value for every bundle you might receive, and its difficult to pin down a number. In an ascending price auction, all you need to do is be able to point to your favorite good (or bundle of goods) that you would buy if the current prices were the final prices, which is often an easier task. 
2. An ascending price auction can end without you having to reveal your full type. For example, in a single item second price auction, the highest bidder never has to reveal (even to the auctioneer) his value for the good -- only that it is higher than that of the second highest bidder. Hence, people might prefer such auctions for "privacy" reasons. 

In an ascending price auction, "truthful" reporting doesn't make sense, since nobody ever asks you to report your type. But we can ask for "sincere bidding", in which bidders truthfully bid on the item at each round that is their favorite, given the current prices. But there is a problem: we typically can't implement sincere bidding as a dominant strategy, because of the problem of threats. Consider the following simple example:

Suppose we have two unit demand bidders 1 and 2, and two goods for sale a and b. We have v_{1,a} = 1, v_{1,b} = epsilon and v_{2,a} = 1/2, v_{2, b} = 1/2 - \epsilon. Suppose moreover that bidder 2 takes the following strategy: "Bid on good a. If bidder 1 bids on good a, then outbid him on whatever he bids on until the price is > 1.'' Against this strategy, bidder 1 cannot obtain non-negative utility if he bids on his favorite good (a), and so his best response is to place an insincere bid on good 2. Moreover, bidder 2 has a clear motivation to take this threatening position -- he obtains substantially higher payoff than if players followed sincere bidding, since he gets his most preferred good without any competition. As a result of instances like these, typically ascending price auctions can implement sincere bidding at best as an (ex-post) Nash equilibirum. 

In this lecture, we talk about how to implement an ascending auction such that the prices are differentially private in the bidding strategies of the players (and the allocation in the end is jointly differentially private). This fixes two of the problems above:

1. The privacy guaranteed by the ascending price auction is no longer hand-wavy and qualitative, but rather precise and quantitative. 
2. We get sincere bidding as an asymptotic ex-post dominant strategy for all players.

To get this result, we need only a mild large-market assumption: that the "supply" of each good is modestly large compared to the number of different types of goods -- but crucially we need to assume nothing about how bidder preferences are generated. 

The intuition, which we will appeal to again later, is that by running the auction privately, we have eliminated the possibility that players can distort incentives by threatening each other.

Lecture 9 -- Purchasing Private Data from Privacy Sensitive Individuals

Yesterday in our privacy and mechanism design course, we were fortunate to have a guest lecture by David Xiao. David told us his exciting recent paper, with Kobbi Nissim and Salil Vadhan, Redrawing the Boundaries on Purchasing Private Data from Privacy-Sensitive Individuals.

Consider the following scenario: An analyst wishes to conduct some medical study about an underlying population, but needs to obtain permission from each individual whose data he uses. On the one hand, he needs to buy data from a representative sample of the population so that his study is accurate. On the other hand, he needs to compensate individuals for their privacy costs, and would like to come up with a payment scheme that incentivizes them to report their true privacy costs, rather than inflating them for selfish gain. Finally, he wants the mechanism to be individually rational: that no rational agent should obtain negative utility by interacting with the analyst.

Because individual's costs for privacy are a function of the method by which their reports are used to compute the outcome of the mechanism, rather than just a function of the outcome itself, this takes us outside of a standard mechanism design setting. What makes the problem tricky is that individual's costs for privacy could quite plausibly be correlated with their private data. Suppose the analyst wishes to estimate the fraction of people in some population who have syphilis. It is reasonable to expect that syphilitics will on the whole want to be compensated more than healthy individuals for a loss of privacy. But this means that even computations on agents reported costs for privacy (and independent of agent's supposedly private data) can lead to privacy loss for those agents, and so must be compensated.

Some years ago Arpita Ghosh and I studied this problem, and showed an impossibility result when making some (unreasonably) strong assumptions. One might have hoped that our result could be circumvented with one of several tweaks to the model. But no. David and his coauthors extend this impossibility result to have much wider applicability, making fewer assumptions on what the analyst is able to observe, and far fewer assumptions about the form of the privacy loss function of the agents. Their result is quite robust: Under extremely general circumstances, no truthful individually rational mechanism which makes finite payments can distinguish between two populations, in one of which everyone has syphilis, and in the other of which nobody does. This result says that no mechanism can simultaneously enjoy truthfulness, individual rationality, and non-trivial accuracy properties, and so without drastically relaxing the model of how people might value privacy, you must always give up on one of these.

They do propose one such relaxation, which seems to reduce to something like the assumption that contracting syphilis can only ever cause your costs for privacy to increase, never to decrease. But this is probably not the last word. I think that convincing answers for what to do in the face of their impressive impossibility result are still to be proposed, and is a really interesting question.

Lecture 8 -- Implementing Correlated Equilibria Ex-Post in Incomplete Information Games

After a spring break hiatus, our class on privacy and mechanism design returns (with all of our students working on their course projects!)

In our third and final lecture on using mediators to implement equilibrium of complete information games in settings of incomplete information, we ask how far we can push the agenda of obtaining ex-post implementations via the technique of differentially private equilibrium computation. Recall that last lecture we saw how to do this in large congestion games. Can we get similar results in arbitrary large games?

One obstacle is that we do not know good algorithms for computing Nash equilibria in arbitrary games at all, let alone privately. However, we do know how to compute arbitrarily good approximations to correlated equilibria in arbitrary n player games! In this lecture, we explore the game theoretic implications of private computation of correlated equilibria, and then show how to do it.

The punchline is you can still implement (correlated) equilibria of the complete information game as an ex-post Nash equilibrium of the incomplete information game, but you need a slightly stronger mediator (which has the power to verify player types if they decide to use the mediator).

To accomplish this goal, we introduce a couple of interesting tools: A powerful composition theorem in differential privacy due to Dwork, Rothblum, and Vadhan, and the multiplicative weights (or weighted majority, or polynomial weights, or hedge, or...) algorithm, which is a natural learning dynamic and can be used to quickly compute (coarse) correlated equilibria in arbitrary games.

Next week we will have a guest lecture, combined with our theory seminar, by David Xiao, who will tell us about his exciting recent work on Redrawing the Boundaries on Purchasing Data from Privacy Sensitive Individuals. 

Lecture 7 -- Privacy Preserving Public Information for Sequential Games

Our seventh lecture was given by Jamie Morgenstern, about her very interesting paper joint with Avrim Blum, Ankit Sharma, and Adam Smith.

The birds-eye view is the following:

Suppose players (think financial institutions) take turns sequentially deciding which investments to make, from amongst a feasible set, which can be different for each player. In general, the profit that a player gets from an investment is a decreasing function of how many players previously have made the same investment. (Perhaps these investments are structured like pyramid schemes, where there is a big advantage in getting in early, or perhaps the market is somehow destabilized if there is too much capital invested in it).

We can study this interaction in various information models. In the complete information setting, each player sees exactly how much has been invested in each resource at the time that she arrives, and the unique dominant strategy solution of the game is for each player to invest greedily. They show that this solution achieves a good constant factor approximation to the optimal welfare.

But if the players are financial institutions, then their investments might represent sensitive trade secrets, and they may not want to share this information with others -- in which case the complete information setting seems unrealistic. This could be very bad news however -- if players have no information at all about what has gone on before their arrival, its not hard to cook up plausible sounding behaviors for them which result in disastrous welfare outcomes.

So the paper asks: can we introduce a differentially private signal (so one that necessarily reveals little actionable information about each agent, and therefore one whose introduction the agents have little reason to object to) that nevertheless allows the market to achieve social welfare that approximates OPT.

Skipping over some details, this paper shows that the answer is yes. Making public a differentially private count of how much has been invested in each resource as the game plays out is enough to guarantee that sequential play (studied either as the simple behavioral strategy in which players imagine that the noisy counts are exactly correct, or any solution in which players play only undominated strategies) results in an outcome that has a bounded competitive ratio with OPT.

This paper also contains an interesting technique that will probably be useful in other contexts: they develop a new method of privately maintaining the count of a set of numbers that achieves better additive error as compared to previous work, at the cost of introducing some small multiplicative error. In the application they need counters for in this paper, this modification gives improved overall bounds.

Lecture 6 -- Implementing Nash equilibria ex-post in incomplete information games (Part 2)

In Lecture 6 of our Privacy and Mechanism Design course, we continue our study of the use of differential privacy to implement equilibrium of complete information games -ex post- in settings of incomplete information augmented with an extremely weak "mediator".

Last class, we proved that to accomplish this task, it would be sufficient to design an algorithm that:

1. Satisfied (joint) differential privacy, and...
2. Computed an (asymptotic) Nash equilibrium of the complete information game induced by reported types. 

We also took a brief detour into private algorithmic techniques, and learned how to privately maintain a count on a stream of numbers. 

This class, we partially implement this agenda. We define large games and congestion games, and give an algorithm for privately computing Nash equilibrium in large congestion games, which uses our newly learned ability to count. We conclude that in such games, with the help of a weak mediator, we can enjoy the nice properties of the pure strategy Nash equilibria of these games in the complete information setting, even in incomplete information settings when player types can be arbitrary (i.e. not necessarily drawn from any prior distribution). 

There remains one more lecture in this series -- we will show that if we strengthen the power of our weak mediators somewhat, by giving them the ability to verify reported player types, then we can extend these results to arbitrary large games (i.e. not necessarily congestion games) by privately computing correlated equilibria. 

This last part will have to wait a couple of weeks though. Next week, we will have Jamie Morgenstern giving us a guest lecture on her very interesting recent work joint with Avrim Blum, Ankit Sharma, and Adam Smith. 

Lecture 4 -- The Empirical Implications of Privacy Aware Choice

Just barely out of order, the notes for Lecture 4 of our privacy and mechanism design class are now online.

In this lecture, Rachel Cummings told us about her very interesting work with Federico Echenique and Adam Wierman, studying what implications preferences for privacy might have in the revealed preferences setting.

The idea, in a nutshell, is this: suppose some entity is observing all of your purchase decisions online, and trying to deduce from them what your utility function over goods is. For example, if it observes you purchasing beer when you could have had milk for the same price, it will deduce that you strictly prefer beer to milk.

Now suppose that you understand that you are being observed, and you have preferences not only over the goods that you buy, but also over the set of deductions that the observer is going to make about you. Given a set of prices and a budget, you will choose which bundle of goods to buy to optimize this tradeoff between your utility for the bundle, and your cost for what is learned about you by the observer. As always, however, the observer only gets to see what you buy.

Can the observer tell whether or not you care about privacy? Can he deduce what your preferences over goods are? Can he prove that you are not buying goods totally at random?

One of the main results discussed in this lecture, is that for sufficiently general forms of the preferences that agents may hold, the answer to all of these questions is "no". Specifically, all sets of observations are rationalizable by some privacy-aware utility function.

Lecture 5 -- Implementing Nash equilibria ex-post in incomplete information games (Part 1)

Welcome back (after a brief hiatus) to the privacy and mechanism design course. Last week we had a guest lecture by Rachel Cummings about her work on the Empirical Implications of Privacy Aware Choice.  We will have notes and a blog post about that soon, but for now, welcome to Lecture 5!

In this lecture, we consider the following problem. Suppose we have an n player game. We might want to implement a Nash equilibrium of the complete information game (which often have nice properties), but naturally find ourselves in the common situation when the n players do not know each others types. Is there a modification of the game that can implement the complete-information game equilibrium as a simple ex-post Nash equilibrium, which does not require that players know anything about each others types, and which requires no coordination?

The modification of the game we consider is the introduction of a very weak "mediator", which essentially only has the power to listen and to give advice, but not to verify or to enforce. Players will have the option of reporting their type to the mediator, in which case it will suggest an action for them to play. However, they can:

1. Completely ignore the mediator and choose an action to play on their own
2. Lie to the mediator about their types, and/or
3. Use the mediator's suggestion however they like, not necessarily following it (i.e. the mediator can not enforce its suggestion)

What we would like is that players should all follow "good behavior", which involves

1. Truthfully reporting their type to the mediator, and then
2. Faithfully following the mediator's suggestion.

We prove that if the mediator offers its suggestions by computing a Nash equilibrium of the complete information game defined by players reported types, and satisfies (a variant of) differential privacy, then the mediator makes "good behavior" an asymptotic ex-post Nash equilibrium of the incomplete information game, and that in this ex-post equilibrium, players end up playing a Nash equilibrium of the original game of complete information (defined by the realized player types).

This leaves us with the minor task of actually figuring out how to compute a Nash equilibrium privately. Here, we realize that thus far in the class, we have been skating by knowing nothing about private algorithm design except for the exponential mechanism. So we take a detour to learn some more basics. We get as far as learning how to count, which turns out to be enough. This will set us up for next lecture, when we can actually implement this agenda and design a mediator that satisfies the hypotheses we need.

(The idea of designing a mediator by privately computing an equilibrium comes from joint work with Michael Kearns, Mallesh Pai, and Jon Ullman, which shows how to privately compute correlated equilibria in arbitrary large games. We will cover this later. The implication in this lecture about mediators that privately compute Nash equilibria comes from joint work with Ryan Rogers, which shows how to privately compute Nash equilibria in large congestion games. )

Lecture 3 -- Mechanism Design for arbitrary objective functions, and without money!

In the third lecture of our course on privacy and mechanism design, we go back to using differential privacy as a tool in mechanism design, and cover a remarkable result of Nissim, Smorodinsky, and Tennenholtz.

Traditionally in mechanism design, social welfare holds a special place in the pantheon of objective functions: this is because in any social choice setting, we can use the VCG mechanism to exactly optimize for social welfare while guaranteeing dominant strategy truthfulness. In general, it is not possible to truthfully optimize most other objective functions -- and even for social welfare, the VCG mechanism requires the ability to charge payments. It is the rare setting when we can achieve some objective truthfully without payments, and even rarer when that objective is not social welfare.

In todays lecture, we give a general mechanism that in any social choice setting (satisfying certain technical conditions) approximately optimizes any low-sensitivity objective function (social welfare satisfies this condition, but so do many others). Moreover, this mechanism is strictly dominant strategy truthful, and crucially does not require the use of payments. Of course, we can't get around classical impossibility results for free -- the tradeoff, as always, is that we are only optimizing our objective approximately up to some additive loss. However, in large economies, this loss will often become negligible as the size of the population grows.

After class, Rachel Cummings will give our theory seminar on her own work in privacy and mechanism design: The Empirical Implications of Privacy Aware Choice, which is joint work with Federico Echenique and Adam Wierman, both from Caltech. Be there or be square!

Lecture 2: Privacy as a Desideratum in Mechanism Design -- Making the Exponential Mechanism Truthful

For those of you following the privacy and mechanism design course at home, tomorrow's Lecture 2 is now online.

This lecture explores a different aspect of privacy and mechanism design. Last week, we considered the use of differential privacy purely as a tool, to design a prior free asymptotically truthful and revenue optimal mechanism for digital goods auctions. In this lecture, we motivate differential privacy as a desideratum for its own sake, and argue that it gives mechanisms (often at very little cost) a natural notion of robustness against the possibility of extra unmodeled parts of agents utility functions.

Finally, we derive a private version of the VCG mechanism, that for general social choice problems is simultaneously:

1. (Exactly) dominant strategy truthful
2. Differentially private
3. (Approximately) welfare optimal

This result is from Huang and Kannan 2012: "The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal". Although this is a recent paper, it is a basic, important, foundational result that "should" have been discovered earlier. It fits in very nicely at the beginning of the semester.

(And for those of you actually taking this class and looking for inspiration to do a course project, this paper started as Zhiyi Huang's course project in the 2011 privacy course I taught here at Penn)

Privacy + Mechanism Design course begins today

Today several students will endure the first (3 hour!) lecture in an experimental course I am teaching on privacy and mechanism design. Its a very new area -- whether or not there is enough material to cover a whole semester may depend on how many new theorems are proven during the semester that the course is running. (I already know of the existence of several papers I will want to teach, but haven't read yet since they aren't yet available!)

A secondary goal that I have is to produce a nice set of lecture notes, that will be accessible to people curious about getting into the field. I encourage people to read along, starting with today's Lecture 1. We're starting from basics -- I don't want to assume that readers know anything about either privacy, or mechanism design. In the first lecture, we introduce differential privacy from the perspective of a game theorist, and use it to solve an interesting problem: prior-free revenue maximization in a digital goods auction. Along the way we learn about a useful tool, "The exponential mechanism", that we will encounter again.

The digital goods auction setting is not only a nice introduction to many of the ideas underlying the privacy/mechanism design connection, it is also historically faithful: all of the results in Lecture 1 are from the seminal paper of McSherry and Talwar which introduced the connection between differential privacy and game theory: Mechanism Design via Differential Privacy.

COLT call for papers

Nina Balcan asked me to post the COLT 2014 call for papers. A couple of interesting things in the call: privacy is specifically mentioned as a constraint of interest on learning, and there is a call for papers on "Learning in other settings: e.g. social, economic, and game-theoretic".

The 27th Annual Conference on Learning Theory (COLT 2014) will take
place in Barcelona, Spain, on June 13-15, 2014

We invite submissions of papers addressing theoretical aspects of
machine learning and related topics. Submissions by authors who are
new to COLT are encouraged. We strongly support a broad definition of
learning theory, including, but not limited to:

• Design and analysis of learning algorithms and their generalization ability
• Computational complexity of learning
• Optimization procedures for learning
• Unsupervised, semi-supervised learning, and clustering
• Online learning
• Interactive learning
• Kernel Methods
• High dimensional and non-parametric empirical inference, including
sparsity methods
• Planning and control, including reinforcement learning
• Learning with additional constraints: E.g. privacy, time or memory
budget, communication
• Learning in other settings: E.g. social, economic, and game-theoretic
• Analysis of learning in related fields: natural language processing,
neuroscience, bioinformatics, privacy and security, machine vision,
data mining, information retrieval.

We are also interested in papers that include viewpoints that are new
to the COLT community. We welcome experimental and algorithmic papers
provided they are relevant to the focus of the conference by
elucidating theoretical results. Also, while the primary focus of the
conference is theoretical, papers can be strengthened by the inclusion
of relevant experimental results.

COLT will award both best paper and best student paper awards. Best
student papers must be authored or coauthored by a student. Authors
must indicate (using a footnote on the first page of the paper) at
submission time if they wish their paper to be eligible for a student
award. This does not preclude the paper to be eligible for the best
paper award. The program committee may decline to make these awards,
or may split them among several papers.

Papers that have previously appeared in journals or at other
conferences, or that are being submitted to other conferences, are not
appropriate for COLT. Papers that include work that has already been
submitted for journal publication may be submitted to COLT, as long as
the papers have not been accepted for publication by the COLT
submission deadline (conditionally or otherwise) and that the paper is
not expected to be published before the COLT conference (June 2014).

Accepted papers will be published electronically, in the JMLR Workshop
and Conference Proceedings series.

Rebuttal Phase
As in the previous years, we will have a rebuttal phase during the
review process. Initial reviews will be sent to authors before final
decisions have been made. Authors will have the opportunity to provide
a short response on the PC's initial evaluation. Final
acceptance/rejection decision will be made a week later.

Open Problems Session:
We also invite submission of open problems. A separate call for open
problems will be available at the conference website:
http://orfe.princeton.edu/conferences/colt2014/

Submission Instructions:
Submissions are limited to 12 JMLR-formatted pages, plus additional
pages for references and appendices. All details, proofs and
derivations required to substantiate the results must be included in
the submission, possibly in the appendices. However, the contribution,
novelty and significance of submissions will be judged primarily based
on the main text (without appendices), and so enough details,
including proof details, must be provided in the main text to convince
the reviewers of the submissions' merits.

Important Dates:
• Paper submission deadline: February 7th, 2014, 11:00 PM EST
• Author response period: April 5-10, 2014
• Author notification: April 19, 2014
• Conference: June 13-15, 2014

On behalf of the COLT 2014 organizers,

Program Chairs
• Maria-Florina Balcan (Georgia Institute of Technology)
• Csaba Szepesvári (University of Alberta)

Local Arrangements Chairs
•  Sébastien Bubeck (Princeton University)
•  Gábor Lugosi (ICREA and Pompeu Fabra University)

Publication Chair
• Vitaly Feldman (IBM Almaden Research Center)

Call for Postdocs

Penn's new Warren Center for Network and Data Sciences (warrencenter.upenn.edu) has multiple postdoc positions for the 2014-15 academic year and beyond. The application procedure (described below) requires candidates to be nominated internally by Center faculty affiliates, so interested candidates should first contact potential Penn faculty hosts in their areas of interest to facilitate a potential nomination.

Michael Kearns and Rakesh Vohra Directors, Warren Center for Network and Data Sciences warrencenter.upenn.edu

**************************************************************************************************************************************************************************

Penn's newly-launched Warren Center for Network and Data Sciences seeks nominations for 2014 Warren Postdoctoral Fellowships.

Warren Fellow candidates should have research interests in the subjects supported by the center, which include but are not limited to network science (including the study of social, technological, economic, organizational and biological networks, as well as underlying foundational areas such as graph theory, game theory, mechanism design) and data science (including machine learning, statistics, data privacy and security). The ideal candidate will have a strongly interdisciplinary research agenda with a demonstrated track record, and would be nominated by faculty affiliates of the Warren Center in two or more Penn departments who will act as hosts, advisors and collaborators of the candidate.

Warren Postdoctoral Fellows will receive generous and competitive stipends and research support, and will participate in a vibrant and growing community of Warren Center faculty affiliates, postdocs and students. We expect to fund multiple Warren Fellows for the 2014-15 academic year. Fellowships are for a one-year period, extendable to two by mutual agreement. In cases where the nominator or their department have partial funding for a nominee, the Warren Center may consider providing additional support to cover the balance of the costs.

Nominations from Penn faculty members affiliated with the Warren Center will be accepted immediately. The nominator's home department is expected to provide office space, administrative support and handle the logistics of employment of a successful candidate, including visa/immigration support where relevant. The nominator should send the following materials to admin@warrencenter.upenn.edu:

* A nomination letter indicating why the candidate is particularly suited to advance the goals of the Warren Center. * A supporting letter from the chair of the nominee's department outlining departmental support that will be provided. * Support letters from one or more other Warren Center faculty affiliates. * The candidate's CV, the candidate's external letters of reference, and a sample of the candidate's work (either as an electronic document or URL).

Please ensure all attachments are in .pdf format.

A committee to reviewing and select applications will be announced shortly. Selections will be made on a periodic and rolling basis, with the expectation that the first class of Fellows will begin in the Fall of 2014.

Michael Kearns and Rakesh Vohra Directors, 
Warren Center for Network and Data Sciences 
warrencenter.upenn.edu

Coordination when Information is Scarce: How Privacy can Help.

This post is the first in a (hopefully) series of posts about how tools and ideas from differential privacy can be useful in solving problems in game theory. The connection might at first be surprising, but is in fact very natural. The field of differential privacy studies algorithms whose inputs are generated by the reports of \(n\) players. It provides tools for bounding the sensitivity of the output of the algorithm in a precise, probabilistic sense to unilateral changes to the input by a single one of these players. This notion of unilateral deviations is very similar to the notions of stability at equilibrium that game theory is concerned about, and this is the root of the connection. For a general overview of the area, let me plug the survey on Differential Privacy and Mechanism Design that Mallesh and I wrote for the most recent issue of SIGecom Exchanges. In this post, I'll discuss a result that Michael Kearns, Mallesh Pai, Jon Ullman, and I have had kicking around for awhile. We only recently hit upon the interpretation of the result that I'll discuss here though, which I rather like. For more details, you can check out the arXiv paper, which we revised a couple of weeks ago. I should add that the story that accompanies our technical contributions is the result of discussions with many people as we've gone about and presented it. Tim Roughgarden and Ricky Vohra deserve special thanks.



In game theory, there are several popular abstractions for what players in a game know about their opponents.

• In games of complete information, players know exactly the utility functions that each of their opponents is trying to optimize. 
• In games of incomplete information, players don't know what their opponent's utility functions are. In Bayesian games, players utility functions are parameterized by "types", which are drawn from a known (possibly correlated) prior distribution. Agents know the distribution from which their opponents' types are drawn, but not the types themselves. 

In games of complete information, the standard solution concept is the Nash equilibrium: informally, everyone should be playing an action such that no single player can benefit by making a unilateral deviation. Players can randomize, so actions are evaluated in expectation over the random choices of one's opponents, but their utility functions are known.

In games of incomplete information, strategies are thought of as mappings from types to actions. The standard solution concept is the "Bayes Nash Equilibrium", which informally states that everyone should be playing a strategy such that no single player can benefit by making a unilateral deviation, where now strategies are evaluated in expectation both over the random choices of one's opponents, and also over the random realization of the types of one's opponents, as drawn from the known prior distribution.

Games of complete information are attractive for a number of reasons: not least of which that they are much cleaner and more analytically tractable than games of incomplete information. However, when talking about large \(n\) player games, where players don't all know each other, have limited abilities to communicate, and might think of their types as proprietary information, games of incomplete information are probably a more reasonable model of reality.

Unfortunately, the quality of Bayes Nash Equilibria can be much worse than the corresponding Nash equilibria of the full information game, even in the worst case over type realizations. The reason is that not knowing the utility functions of your opponents can make coordination very difficult. Consider the following toy example, borrowed from Bhawalkar and Roughgarden:

There are \(n\) players, and \(n + \sqrt{n}\) "goods" to be distributed. Each player \(i\) has utility \(u_{i,j} \in \{0,1\}\) for receiving a good \(j\). The game is played as follows: each player \(i\) names a single good \(s_i\). Each good \(j\) is allocated at random to one of the players that named it. Now suppose that types are drawn from the following distribution. The goods are randomly partitioned into two sets, \(S\) and \(T\), with \(|S| = n\) and \(|T| = \sqrt{n}\). For every player \(i\) and good \(j \in T\), \(u_{i,j} = 1\). A perfect matching \(\mu\) is selected at random between agents \(i\) and goods in \(S\). Agents have value \(u_{i,\mu(i)} = 1 \) for the good \(\mu(i) \in S\) that they are matched to, and value \(u_{i,j} = 0\) for every good \(j \neq \mu(i)\) in \(S\) that they are not matched to. In other words, every player has a "special" good in \(S\) that she uniquely desires, and everyone desires all of the goods in \(T\). If we are in the complete information setting, then since everyone has the option of requesting their special good \(s_i = \mu(i)\), in any reasonable equilibrium (with nobody requesting a good they don't want) \(n\) goods are allocated to bidders who desire them, for total social welfare of \(n\). However, in the incomplete information setting, because of the symmetry of the distribution, no player can distinguish their special good from amongst the \(\sqrt{n} + 1\) goods that they value. Its not hard to see that in this case, in equilibrium only \(O(\sqrt{n})\) goods get allocated.

So if we find ourselves in a setting of incomplete information, we might nevertheless prefer to implement an equilibrium of the game of complete information defined by the realized types of the players. How can we do that, especially if we have limited power to modify the game?

One tempting solution is just to augment the game to allow players to publicly announce their types (and thus make the game one of complete information). Of course equilibria of the complete information game might not be unique, so to help solve the coordination problem, we could introduce a weak "proxy" that players can choose whether or not to use. Players can "opt in" to the proxy, which means that they report their type to the proxy, which then recommends an action for them to play. At this point they are free to follow the recommendation, or not. Alternately, they can "opt out" of the proxy, which means they never report their type, and then just choose an action on their own. It would be nice if we could design a proxy such that:

1. Simultaneously for every prior on agent types, it is a Bayes-Nash equilibrium for agents to opt-in to the proxy, and then follow its suggested action, and
2. Given that all players behave as in (1), that the resulting play forms an equilibrium of the complete information game induced by the actual, realized types of the players. 

Its tempting to think that to design such a proxy, it is sufficient to have it compute a Nash equilibrium of the complete information game defined by types of the players who opt in, and then suggest that each player play her part of this Nash equilibrium. After all, if everyone is opting in and playing their part of a Nash equilibrium, how can you do better than to do the same? By definition, in a Nash equilibrium, your suggested action is a best response given what all other players are playing. And in fact, in the toy allocation example we discussed above, this works, since there is an equilibrium of the complete information game that is simultaneously optimal for all players.

In general, however, this approach fails. The flaw in our reasoning is that by opting out, you change what the proxy is computing: it is now computing a different equilibrium, for a different game, and so by opting out, you are not merely making a unilateral deviation from a Nash equilibrium (which cannot be beneficial), you are potentially dramatically changing what actions all other players are playing. The Nash equilibrium condition does not protect against deviations like that, and in fact its not hard to construct an example in which this is a real problem. Consider, e.g. toy example #2: There are \(n\) players who each have one of two types -- (M)ountain, or (B)each. Each player has two actions -- they can go to the beach, or go to the mountain. Players prefer the activity that corresponds to their own type, but they also like company. So if a \(p\) fraction of people go to the Mountain, an M type gets utility \(10\cdot p\) if he goes to the mountain, and \(5\cdot (1-p)\) if he goes to the beach. A B type gets utility \(5\cdot p\) if she goes to the mountain, and \(10 \cdot (1-p)\) if she goes to the beach. A proxy that suggests that all players go to the beach if type M is in the majority, and otherwise suggests that all agents go to the mountain always computes a Nash equilibrium of the complete information game defined by the reported types. Nevertheless, any player that is pivotal has incentive to opt-out of the proxy, since this causes the proxy to send all other players to her preferred location.

But what if it were possible to compute an equilibrium in such a way so that whether or not any player \(i\) opted in had very little affect on the distribution over actions suggested by the proxy to all other player \(j \neq i\)? In this case, the problem would be solved: any unilateral deviation from the all-opt-in-and-follow-the-proxy's-suggestion solution would not (substantially) affect the play of one's opponents, and so they would all continue playing their part of an equilibrium of the complete information game, defined on all player's realized types. The equilibrium condition would now directly guarantee that such a deviation could not be beneficial.

So to design a good proxy, its not enough to just have an algorithm that computes an equilibrium of the game defined by the reported types, but it is enough if that algorithm also satisfies a strong enough stability condition. It turns out that a sufficient "stability" condition is a variant on differential privacy: informally, that any unilaterial deviation by a single player \(i\) should not change (by more than a \( (1\pm \epsilon)\) factor) the probability that any particular profile of \(n-1\) actions is suggested to the \(n-1\) players \(j \neq i\).

And in fact it is possible to implement this plan, at least for certain classes of games. We study the class of "large games", which informally, are \(n\) player games in which the affect of any player \(i\)'s action on the utility of any player \(j \neq i \) is bounded by some quantity which is diminishing in \(n\). The Beach/Mountain example is of this type, as are many large population games.  Our main technical result is an algorithm satisfying the required differential privacy stability condition, which computes a correlated equilibrium of any large game. The upshot is that in large games, it is possible to design a very weak proxy (that doesn't have the power to make payments, force players to opt in, or enforce actions once they do opt in) that implements an \(\eta\)-approximate correlated equilibrium of the complete information game, as an \(\eta\)-approximate Bayes Nash equilibrium of the partial information game, no matter what the prior distribution on agent types is. Here \(\eta\) is some approximation parameter that is tending to zero in the size of the game -- i.e. as the game grows large, the equilibria become exact.

To emphasize the purely game theoretic aspects of this problem, I have ignored the fact that differential privacy of course also provides a good guarantee of "privacy". Aside from straightforward incentive issues, there are other reasons why players might be reluctant to announce their types and participate in a complete information game: perhaps their types are valuable trade secrets, or would be embarrassing admissions. Because our solution also happens to provide differential privacy, it is able to implement an equilibrium of the complete information game, while maintaining the privacy properties inherent in a game of incomplete information.

To conclude, differential privacy thus far has been primarily a problem-driven field, that has borrowed techniques from many other areas to solve problems in private data analysis. But in the process, it has also built up a strong conceptual and technical tool kit for thinking about the stability of randomized algorithms to small changes in their inputs. I hope that this and future posts serve to convince you that there is something to be gained by borrowing the tools of differential privacy and applying them to solve problems in seemingly unrelated fields.

Registration for EC is now open

Registration for EC 2013 is now open: http://www.sigecom.org/ec13/registration.html

Register before May 29 to get the early registration discount.

One day workshop in NYC on Differential Privacy, Social Science, and Economics

If you are in the New York City area and interested in the intersection of privacy, economics, and the social sciences, you should check out a workshop being held on March 7th at the Simons Foundation. It is open to the public, and tickets are free, but you must register by the end of February: http://econandsocialsciences.eventbrite.com/

I'll be giving a tutorial on differential privacy in the morning (no background assumed), and the rest of the day will be devoted to talks and discussion by a number of illustrious economists and social scientists. It should be lots of fun.

Differential privacy videos online!

Have you always wanted to learn about differential privacy, but haven't had the time/motivation to read all of the papers? Do you have 3 hours to kill? Well you are in luck! There are now 3 excellent tutorial videos online for you to enjoy! These are from the DIMACS workshop that Adam Smith and I ran last month.

1. Moritz Hardt gives a tutorial on multiplicative weights in differential privacy: http://youtu.be/VeY-fqaaQv4
2. Gerome Miklau gives a tutorial on the matrix mechanism and related work in differential privacy: http://youtu.be/FCIoJ77aTQ4
3. Benjamin Pierce gives a tutorial on differentially private programming languages: http://youtu.be/ci2aueqZ6CU
4. I give a tutorial on game theory and differential privacy: http://youtu.be/kqQ2qv0fYtQ

These tutorials all assume some familiarity with differential privacy (I don't think differential privacy is actually -defined- in any of them). For some light reading to fill in some of the background, you can check out my course notes.

The Fifth Annual New York Computer Science and Economics Day

Are you going to be near NYC in December? The fifth annual New York Computer Science and Economics Day will be held in the new Simons Foundation auditorium in NYC on Monday, December 3rd. The theme for this year is "The Economics of Big Data, Information, and Privacy". In addition to a terrific lineup of invited speakers, posters and short talks (up to 10 minutes long) are invited from students. Abstracts for these should be submitted by November 5th. (Conveniently, right after the STOC deadline). 

See the website for more information: nyce1212

DIMACS Workshop on Differential Privacy and Call for Student Participation

Adam Smith and I are running a 3 day interdisciplinary workshop on differential privacy at DIMACS (Rutgers), on October 24-26. This is immediately following FOCS, which is also being held at Rutgers. The workshop will begin with a day of tutorials on differential privacy as understood in various communities (Theory, databases, programming languages, and game theory), and will continue with two days of research talks and discussion. Details of the workshop can be found here: http://dimacs.rutgers.edu/Workshops/DifferentialPrivacy/ We have an extremely exciting program. (The program listed on the website is somewhat out of date -- there are a half dozen or so additional speakers confirmed).

As part of the program, we will also have a session of short (5-10 minute) talks from students, postdocs, and other interested parties. We encourage submission of abstracts for short talks. The solicitation is below.

See you all in October!


DIMACS Workshop on Differential Privacy across Computer Science
October 24-26, 2012
(immediately after FOCS 2012)

Call for Abstracts -- Short Presentations

The upcoming DIMACS workshop on differential privacy will feature
invited talks by experts from a range of areas in computer science as
well as short talks (5 to 10 minutes) by participants.

Participants interested in giving a short presentation should send an
email to asmith+dimacs@psu.edu containing a proposed talk title,
abstract, and the speaker's name and affiliation.  We wil try to
accommodate as many speakers as possible, but
a) requests received before October 1 will get full consideration
b) priority will be given to junior researchers, so students and
postdocs should indicate their status in the email.

More information about the workshop:

The last few years have seen an explosion of results concerning
differential privacy across many distinct but overlapping communities
in computer science: Theoretical Computer Science, Databases,
Programming Languages, Machine Learning, Data Mining, Security, and
Cryptography. Each of these different areas has different priorities
and techniques, and despite very similar interests, motivations, and
choice of problems, it has become difficult to keep track of this
large literature across so many different venues. The purpose of this
workshop is to bring researchers in differential privacy across all of
these communities together under one roof to discuss recent results
and synchronize our understanding of the field. The first day of the
workshop will include tutorials, representing a broad cross-section of
research across fields. The remaining days will be devoted to talks on
the exciting recent results in differential privacy across
communities, discussion and formation of interesting open problems,
and directions for potential inter-community collaborations.

A tentative program and registration information can be found at
http://dimacs.rutgers.edu/Workshops/DifferentialPrivacy/