488 research outputs found
Truthful Linear Regression
We consider the problem of fitting a linear model to data held by individuals
who are concerned about their privacy. Incentivizing most players to truthfully
report their data to the analyst constrains our design to mechanisms that
provide a privacy guarantee to the participants; we use differential privacy to
model individuals' privacy losses. This immediately poses a problem, as
differentially private computation of a linear model necessarily produces a
biased estimation, and existing approaches to design mechanisms to elicit data
from privacy-sensitive individuals do not generalize well to biased estimators.
We overcome this challenge through an appropriate design of the computation and
payment scheme.Comment: To appear in Proceedings of the 28th Annual Conference on Learning
Theory (COLT 2015
Truthful Mechanisms for Agents that Value Privacy
Recent work has constructed economic mechanisms that are both truthful and
differentially private. In these mechanisms, privacy is treated separately from
the truthfulness; it is not incorporated in players' utility functions (and
doing so has been shown to lead to non-truthfulness in some cases). In this
work, we propose a new, general way of modelling privacy in players' utility
functions. Specifically, we only assume that if an outcome has the property
that any report of player would have led to with approximately the same
probability, then has small privacy cost to player . We give three
mechanisms that are truthful with respect to our modelling of privacy: for an
election between two candidates, for a discrete version of the facility
location problem, and for a general social choice problem with discrete
utilities (via a VCG-like mechanism). As the number of players increases,
the social welfare achieved by our mechanisms approaches optimal (as a fraction
of )
Exploiting Weak Supermodularity for Coalition-Proof Mechanisms
Under the incentive-compatible Vickrey-Clarke-Groves mechanism, coalitions of
participants can influence the auction outcome to obtain higher collective
profit. These manipulations were proven to be eliminated if and only if the
market objective is supermodular. Nevertheless, several auctions do not satisfy
the stringent conditions for supermodularity. These auctions include
electricity markets, which are the main motivation of our study. To
characterize nonsupermodular functions, we introduce the supermodularity ratio
and the weak supermodularity. We show that these concepts provide us with tight
bounds on the profitability of collusion and shill bidding. We then derive an
analytical lower bound on the supermodularity ratio. Our results are verified
with case studies based on the IEEE test systems
Budget-Feasible Mechanism Design for Non-Monotone Submodular Objectives: Offline and Online
The framework of budget-feasible mechanism design studies procurement
auctions where the auctioneer (buyer) aims to maximize his valuation function
subject to a hard budget constraint. We study the problem of designing truthful
mechanisms that have good approximation guarantees and never pay the
participating agents (sellers) more than the budget. We focus on the case of
general (non-monotone) submodular valuation functions and derive the first
truthful, budget-feasible and -approximate mechanisms that run in
polynomial time in the value query model, for both offline and online auctions.
Prior to our work, the only -approximation mechanism known for
non-monotone submodular objectives required an exponential number of value
queries.
At the heart of our approach lies a novel greedy algorithm for non-monotone
submodular maximization under a knapsack constraint. Our algorithm builds two
candidate solutions simultaneously (to achieve a good approximation), yet
ensures that agents cannot jump from one solution to the other (to implicitly
enforce truthfulness). Ours is the first mechanism for the problem
where---crucially---the agents are not ordered with respect to their marginal
value per cost. This allows us to appropriately adapt these ideas to the online
setting as well.
To further illustrate the applicability of our approach, we also consider the
case where additional feasibility constraints are present. We obtain
-approximation mechanisms for both monotone and non-monotone submodular
objectives, when the feasible solutions are independent sets of a -system.
With the exception of additive valuation functions, no mechanisms were known
for this setting prior to our work. Finally, we provide lower bounds suggesting
that, when one cares about non-trivial approximation guarantees in polynomial
time, our results are asymptotically best possible.Comment: Accepted to EC 201
Bounding the Optimal Revenue of Selling Multiple Goods
Using duality theory techniques we derive simple, closed-form formulas for
bounding the optimal revenue of a monopolist selling many heterogeneous goods,
in the case where the buyer's valuations for the items come i.i.d. from a
uniform distribution and in the case where they follow independent (but not
necessarily identical) exponential distributions. We apply this in order to get
in both these settings specific performance guarantees, as functions of the
number of items , for the simple deterministic selling mechanisms studied by
Hart and Nisan [EC 2012], namely the one that sells the items separately and
the one that offers them all in a single bundle.
We also propose and study the performance of a natural randomized mechanism
for exponential valuations, called Proportional. As an interesting corollary,
for the special case where the exponential distributions are also identical, we
can derive that offering the goods in a single full bundle is the optimal
selling mechanism for any number of items. To our knowledge, this is the first
result of its kind: finding a revenue-maximizing auction in an additive setting
with arbitrarily many goods
Budget Feasible Mechanisms for Experimental Design
In the classical experimental design setting, an experimenter E has access to
a population of potential experiment subjects , each
associated with a vector of features . Conducting an experiment
with subject reveals an unknown value to E. E typically assumes
some hypothetical relationship between 's and 's, e.g., , and estimates from experiments, e.g., through linear
regression. As a proxy for various practical constraints, E may select only a
subset of subjects on which to conduct the experiment.
We initiate the study of budgeted mechanisms for experimental design. In this
setting, E has a budget . Each subject declares an associated cost to be part of the experiment, and must be paid at least her cost. In
particular, the Experimental Design Problem (EDP) is to find a set of
subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in
S}x_i\T{x_i}) under the constraint ; our objective
function corresponds to the information gain in parameter that is
learned through linear regression methods, and is related to the so-called
-optimality criterion. Further, the subjects are strategic and may lie about
their costs.
We present a deterministic, polynomial time, budget feasible mechanism
scheme, that is approximately truthful and yields a constant factor
approximation to EDP. In particular, for any small and , we can construct a (12.98, )-approximate mechanism that is
-truthful and runs in polynomial time in both and
. We also establish that no truthful,
budget-feasible algorithms is possible within a factor 2 approximation, and
show how to generalize our approach to a wide class of learning problems,
beyond linear regression
Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity
We study the revenue maximization problem of a seller with n heterogeneous
items for sale to a single buyer whose valuation function for sets of items is
unknown and drawn from some distribution D. We show that if D is a distribution
over subadditive valuations with independent items, then the better of pricing
each item separately or pricing only the grand bundle achieves a
constant-factor approximation to the revenue of the optimal mechanism. This
includes buyers who are k-demand, additive up to a matroid constraint, or
additive up to constraints of any downwards-closed set system (and whose values
for the individual items are sampled independently), as well as buyers who are
fractionally subadditive with item multipliers drawn independently. Our proof
makes use of the core-tail decomposition framework developed in prior work
showing similar results for the significantly simpler class of additive buyers
[LY13, BILW14].
In the second part of the paper, we develop a connection between
approximately optimal simple mechanisms and approximate revenue monotonicity
with respect to buyers' valuations. Revenue non-monotonicity is the phenomenon
that sometimes strictly increasing buyers' values for every set can strictly
decrease the revenue of the optimal mechanism [HR12]. Using our main result, we
derive a bound on how bad this degradation can be (and dub such a bound a proof
of approximate revenue monotonicity); we further show that better bounds on
approximate monotonicity imply a better analysis of our simple mechanisms.Comment: Updated title and body to version included in TEAC. Adapted Theorem
5.2 to accommodate \eta-BIC auctions (versus exactly BIC
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