3,513 research outputs found
Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy
Game theory has emerged as a fruitful paradigm for the design of networked
multiagent systems. A fundamental component of this approach is the design of
agents' utility functions so that their self-interested maximization results in
a desirable collective behavior. In this work we focus on a well-studied class
of distributed resource allocation problems where each agent is requested to
select a subset of resources with the goal of optimizing a given system-level
objective. Our core contribution is the development of a novel framework to
tightly characterize the worst case performance of any resulting Nash
equilibrium (price of anarchy) as a function of the chosen agents' utility
functions. Leveraging this result, we identify how to design such utilities so
as to optimize the price of anarchy through a tractable linear program. This
provides us with a priori performance certificates applicable to any existing
learning algorithm capable of driving the system to an equilibrium. Part II of
this work specializes these results to submodular and supermodular objectives,
discusses the complexity of computing Nash equilibria, and provides multiple
illustrations of the theoretical findings.Comment: 15 pages, 5 figure
Approximately Truthful Multi-Agent Optimization Using Cloud-Enforced Joint Differential Privacy
Multi-agent coordination problems often require agents to exchange state
information in order to reach some collective goal, such as agreement on a
final state value. In some cases, it is feasible that opportunistic agents may
deceptively report false state values for their own benefit, e.g., to claim a
larger portion of shared resources. Motivated by such cases, this paper
presents a multi-agent coordination framework which disincentivizes
opportunistic misreporting of state information. This paper focuses on
multi-agent coordination problems that can be stated as nonlinear programs,
with non-separable constraints coupling the agents. In this setting, an
opportunistic agent may be tempted to skew the problem's constraints in its
favor to reduce its local cost, and this is exactly the behavior we seek to
disincentivize. The framework presented uses a primal-dual approach wherein the
agents compute primal updates and a centralized cloud computer computes dual
updates. All computations performed by the cloud are carried out in a way that
enforces joint differential privacy, which adds noise in order to dilute any
agent's influence upon the value of its cost function in the problem. We show
that this dilution deters agents from intentionally misreporting their states
to the cloud, and present bounds on the possible cost reduction an agent can
attain through misreporting its state. This work extends our earlier work on
incorporating ordinary differential privacy into multi-agent optimization, and
we show that this work can be modified to provide a disincentivize for
misreporting states to the cloud. Numerical results are presented to
demonstrate convergence of the optimization algorithm under joint differential
privacy.Comment: 17 pages, 3 figure
Quadratic Multi-Dimensional Signaling Games and Affine Equilibria
This paper studies the decentralized quadratic cheap talk and signaling game
problems when an encoder and a decoder, viewed as two decision makers, have
misaligned objective functions. The main contributions of this study are the
extension of Crawford and Sobel's cheap talk formulation to multi-dimensional
sources and to noisy channel setups. We consider both (simultaneous) Nash
equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary
scalar sources, in the presence of misalignment, the quantized nature of all
equilibrium policies holds for Nash equilibria in the sense that all Nash
equilibria are equivalent to those achieved by quantized encoder policies. On
the other hand, all Stackelberg equilibria policies are fully informative. For
multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may
be of non-quantized nature, and even linear. In the noisy setup, a Gaussian
source is to be transmitted over an additive Gaussian channel. The goals of the
encoder and the decoder are misaligned by a bias term and encoder's cost also
includes a penalty term on signal power. Conditions for the existence of affine
Nash equilibria as well as general informative equilibria are presented. For
the noisy setup, the only Stackelberg equilibrium is the linear equilibrium
when the variables are scalar. Our findings provide further conditions on when
affine policies may be optimal in decentralized multi-criteria control problems
and lead to conditions for the presence of active information transmission in
strategic environments.Comment: 15 pages, 4 figure
Development and Analysis of Deterministic Privacy-Preserving Policies Using Non-Stochastic Information Theory
A deterministic privacy metric using non-stochastic information theory is
developed. Particularly, minimax information is used to construct a measure of
information leakage, which is inversely proportional to the measure of privacy.
Anyone can submit a query to a trusted agent with access to a non-stochastic
uncertain private dataset. Optimal deterministic privacy-preserving policies
for responding to the submitted query are computed by maximizing the measure of
privacy subject to a constraint on the worst-case quality of the response
(i.e., the worst-case difference between the response by the agent and the
output of the query computed on the private dataset). The optimal
privacy-preserving policy is proved to be a piecewise constant function in the
form of a quantization operator applied on the output of the submitted query.
The measure of privacy is also used to analyze the performance of -anonymity
methodology (a popular deterministic mechanism for privacy-preserving release
of datasets using suppression and generalization techniques), proving that it
is in fact not privacy-preserving.Comment: improved introduction and numerical exampl
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Differentially-private Distributed Algorithms for Aggregative Games with Guaranteed Convergence
The distributed computation of a Nash equilibrium in aggregative games is
gaining increased traction in recent years. Of particular interest is the
mediator-free scenario where individual players only access or observe the
decisions of their neighbors due to practical constraints. Given the
competitive rivalry among participating players, protecting the privacy of
individual players becomes imperative when sensitive information is involved.
We propose a fully distributed equilibrium-computation approach for aggregative
games that can achieve both rigorous differential privacy and guaranteed
computation accuracy of the Nash equilibrium. This is in sharp contrast to
existing differential-privacy solutions for aggregative games that have to
either sacrifice the accuracy of equilibrium computation to gain rigorous
privacy guarantees, or allow the cumulative privacy budget to grow unbounded,
hence losing privacy guarantees, as iteration proceeds. Our approach uses
independent noises across players, thus making it effective even when
adversaries have access to all shared messages as well as the underlying
algorithm structure. The encryption-free nature of the proposed approach, also
ensures efficiency in computation and communication. The approach is also
applicable in stochastic aggregative games, able to ensure both rigorous
differential privacy and guaranteed computation accuracy of the Nash
equilibrium when individual players only have stochastic estimates of their
pseudo-gradient mappings. Numerical comparisons with existing counterparts
confirm the effectiveness of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:2202.0111
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