619 research outputs found
Conducting Truthful Surveys, Cheaply
We consider the problem of conducting a survey with the goal of obtaining an
unbiased estimator of some population statistic when individuals have unknown
costs (drawn from a known prior) for participating in the survey. Individuals
must be compensated for their participation and are strategic agents, and so
the payment scheme must incentivize truthful behavior. We derive optimal
truthful mechanisms for this problem for the two goals of minimizing the
variance of the estimator given a fixed budget, and minimizing the expected
cost of the survey given a fixed variance goal
Asymptotically Truthful Equilibrium Selection in Large Congestion Games
Studying games in the complete information model makes them analytically
tractable. However, large player interactions are more realistically
modeled as games of incomplete information, where players may know little to
nothing about the types of other players. Unfortunately, games in incomplete
information settings lose many of the nice properties of complete information
games: the quality of equilibria can become worse, the equilibria lose their
ex-post properties, and coordinating on an equilibrium becomes even more
difficult. Because of these problems, we would like to study games of
incomplete information, but still implement equilibria of the complete
information game induced by the (unknown) realized player types.
This problem was recently studied by Kearns et al. and solved in large games
by means of introducing a weak mediator: their mediator took as input reported
types of players, and output suggested actions which formed a correlated
equilibrium of the underlying game. Players had the option to play
independently of the mediator, or ignore its suggestions, but crucially, if
they decided to opt-in to the mediator, they did not have the power to lie
about their type. In this paper, we rectify this deficiency in the setting of
large congestion games. We give, in a sense, the weakest possible mediator: it
cannot enforce participation, verify types, or enforce its suggestions.
Moreover, our mediator implements a Nash equilibrium of the complete
information game. We show that it is an (asymptotic) ex-post equilibrium of the
incomplete information game for all players to use the mediator honestly, and
that when they do so, they end up playing an approximate Nash equilibrium of
the induced complete information game. In particular, truthful use of the
mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.Comment: The conference version of this paper appeared in EC 2014. This
manuscript has been merged and subsumed by the preprint "Robust Mediators in
Large Games": http://arxiv.org/abs/1512.0269
Beating Randomized Response on Incoherent Matrices
Computing accurate low rank approximations of large matrices is a fundamental
data mining task. In many applications however the matrix contains sensitive
information about individuals. In such case we would like to release a low rank
approximation that satisfies a strong privacy guarantee such as differential
privacy. Unfortunately, to date the best known algorithm for this task that
satisfies differential privacy is based on naive input perturbation or
randomized response: Each entry of the matrix is perturbed independently by a
sufficiently large random noise variable, a low rank approximation is then
computed on the resulting matrix.
We give (the first) significant improvements in accuracy over randomized
response under the natural and necessary assumption that the matrix has low
coherence. Our algorithm is also very efficient and finds a constant rank
approximation of an m x n matrix in time O(mn). Note that even generating the
noise matrix required for randomized response already requires time O(mn)
Fast Private Data Release Algorithms for Sparse Queries
We revisit the problem of accurately answering large classes of statistical
queries while preserving differential privacy. Previous approaches to this
problem have either been very general but have not had run-time polynomial in
the size of the database, have applied only to very limited classes of queries,
or have relaxed the notion of worst-case error guarantees. In this paper we
consider the large class of sparse queries, which take non-zero values on only
polynomially many universe elements. We give efficient query release algorithms
for this class, in both the interactive and the non-interactive setting. Our
algorithms also achieve better accuracy bounds than previous general techniques
do when applied to sparse queries: our bounds are independent of the universe
size. In fact, even the runtime of our interactive mechanism is independent of
the universe size, and so can be implemented in the "infinite universe" model
in which no finite universe need be specified by the data curator
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
Selling Privacy at Auction
We initiate the study of markets for private data, though the lens of
differential privacy. Although the purchase and sale of private data has
already begun on a large scale, a theory of privacy as a commodity is missing.
In this paper, we propose to build such a theory. Specifically, we consider a
setting in which a data analyst wishes to buy information from a population
from which he can estimate some statistic. The analyst wishes to obtain an
accurate estimate cheaply. On the other hand, the owners of the private data
experience some cost for their loss of privacy, and must be compensated for
this loss. Agents are selfish, and wish to maximize their profit, so our goal
is to design truthful mechanisms. Our main result is that such auctions can
naturally be viewed and optimally solved as variants of multi-unit procurement
auctions. Based on this result, we derive auctions for two natural settings
which are optimal up to small constant factors:
1. In the setting in which the data analyst has a fixed accuracy goal, we
show that an application of the classic Vickrey auction achieves the analyst's
accuracy goal while minimizing his total payment.
2. In the setting in which the data analyst has a fixed budget, we give a
mechanism which maximizes the accuracy of the resulting estimate while
guaranteeing that the resulting sum payments do not exceed the analysts budget.
In both cases, our comparison class is the set of envy-free mechanisms, which
correspond to the natural class of fixed-price mechanisms in our setting.
In both of these results, we ignore the privacy cost due to possible
correlations between an individuals private data and his valuation for privacy
itself. We then show that generically, no individually rational mechanism can
compensate individuals for the privacy loss incurred due to their reported
valuations for privacy.Comment: Extended Abstract appeared in the proceedings of EC 201
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
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
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