331,882 research outputs found
Mechanism Design via Correlation Gap
For revenue and welfare maximization in single-dimensional Bayesian settings,
Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms
(SPMs), though simple in form, can perform surprisingly well compared to the
optimal mechanisms. In this paper, we give a theoretical explanation of this
fact, based on a connection to the notion of correlation gap.
Loosely speaking, for auction environments with matroid constraints, we can
relate the performance of a mechanism to the expectation of a monotone
submodular function over a random set. This random set corresponds to the
winner set for the optimal mechanism, which is highly correlated, and
corresponds to certain demand set for SPMs, which is independent. The notion of
correlation gap of Agrawal et al.\ (SODA10) quantifies how much we {}"lose" in
the expectation of the function by ignoring correlation in the random set, and
hence bounds our loss in using certain SPM instead of the optimal mechanism.
Furthermore, the correlation gap of a monotone and submodular function is known
to be small, and it follows that certain SPM can approximate the optimal
mechanism by a good constant factor.
Exploiting this connection, we give tight analysis of a greedy-based SPM of
Chawla et al.\ for several environments. In particular, we show that it gives
an -approximation for matroid environments, gives asymptotically a
-approximation for the important sub-case of -unit
auctions, and gives a -approximation for environments with
-independent set system constraints
Smoothness for Simultaneous Composition of Mechanisms with Admission
We study social welfare of learning outcomes in mechanisms with admission. In
our repeated game there are bidders and mechanisms, and in each round
each mechanism is available for each bidder only with a certain probability.
Our scenario is an elementary case of simple mechanism design with incomplete
information, where availabilities are bidder types. It captures natural
applications in online markets with limited supply and can be used to model
access of unreliable channels in wireless networks.
If mechanisms satisfy a smoothness guarantee, existing results show that
learning outcomes recover a significant fraction of the optimal social welfare.
These approaches, however, have serious drawbacks in terms of plausibility and
computational complexity. Also, the guarantees apply only when availabilities
are stochastically independent among bidders.
In contrast, we propose an alternative approach where each bidder uses a
single no-regret learning algorithm and applies it in all rounds. This results
in what we call availability-oblivious coarse correlated equilibria. It
exponentially decreases the learning burden, simplifies implementation (e.g.,
as a method for channel access in wireless devices), and thereby addresses some
of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian
settings. Our main results are general composition theorems for smooth
mechanisms when valuation functions of bidders are lattice-submodular. They
rely on an interesting connection to the notion of correlation gap of
submodular functions over product lattices.Comment: Full version of WINE 2016 pape
Design of electron correlation effects in interfaces and nanostructures
We propose that one of the best grounds for the materials design from the
viewpoint of {\it electron correlation} such as ferromagnetism,
superconductivity is the atomically controlled nanostructures and
heterointerfaces, as theoretically demonstrated here from three examples with
first-principles calculations: (i) Band ferromagnetism in a purely organic
polymer of five-membered rings, where the flat-band ferromagnetism due to the
electron-electron repulsion is proposed. (ii) Metal-induced gap states (MIGS)
of about one atomic monolayer thick at insulator/metal heterointerfaces,
recently detected experimentally, for which an exciton-mechanism
superconductivity is considered. (iii) Alkali-metal doped zeolite, a class of
nanostructured host-guest systems, where ferromagnetism has been experimentally
discovered, for which a picture of the "supercrystal" composed of "superatoms"
is proposed and Mott-insulator properties are considered. These indicate that
design of electron correlation is indeed a promising avenue for nanostructures
and heterointerfaces.Comment: to be published in Proc. 7th Int. Conf. on Atomically Controlled
Surfaces, Interfaces and Nanostructures, Nara, Nov. 2003, 14 pages, 10
figure
Context-Aware Generative Adversarial Privacy
Preserving the utility of published datasets while simultaneously providing
provable privacy guarantees is a well-known challenge. On the one hand,
context-free privacy solutions, such as differential privacy, provide strong
privacy guarantees, but often lead to a significant reduction in utility. On
the other hand, context-aware privacy solutions, such as information theoretic
privacy, achieve an improved privacy-utility tradeoff, but assume that the data
holder has access to dataset statistics. We circumvent these limitations by
introducing a novel context-aware privacy framework called generative
adversarial privacy (GAP). GAP leverages recent advancements in generative
adversarial networks (GANs) to allow the data holder to learn privatization
schemes from the dataset itself. Under GAP, learning the privacy mechanism is
formulated as a constrained minimax game between two players: a privatizer that
sanitizes the dataset in a way that limits the risk of inference attacks on the
individuals' private variables, and an adversary that tries to infer the
private variables from the sanitized dataset. To evaluate GAP's performance, we
investigate two simple (yet canonical) statistical dataset models: (a) the
binary data model, and (b) the binary Gaussian mixture model. For both models,
we derive game-theoretically optimal minimax privacy mechanisms, and show that
the privacy mechanisms learned from data (in a generative adversarial fashion)
match the theoretically optimal ones. This demonstrates that our framework can
be easily applied in practice, even in the absence of dataset statistics.Comment: Improved version of a paper accepted by Entropy Journal, Special
Issue on Information Theory in Machine Learning and Data Scienc
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