692 research outputs found
Error-Correcting Data Structures
We study data structures in the presence of adversarial noise. We want to
encode a given object in a succinct data structure that enables us to
efficiently answer specific queries about the object, even if the data
structure has been corrupted by a constant fraction of errors. This new model
is the common generalization of (static) data structures and locally decodable
error-correcting codes. The main issue is the tradeoff between the space used
by the data structure and the time (number of probes) needed to answer a query
about the encoded object. We prove a number of upper and lower bounds on
various natural error-correcting data structure problems. In particular, we
show that the optimal length of error-correcting data structures for the
Membership problem (where we want to store subsets of size s from a universe of
size n) is closely related to the optimal length of locally decodable codes for
s-bit strings.Comment: 15 pages LaTeX; an abridged version will appear in the Proceedings of
the STACS 2009 conferenc
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
Correlation Clustering with Adaptive Similarity Queries
In correlation clustering, we are given objects together with a binary
similarity score between each pair of them. The goal is to partition the
objects into clusters so to minimise the disagreements with the scores. In this
work we investigate correlation clustering as an active learning problem: each
similarity score can be learned by making a query, and the goal is to minimise
both the disagreements and the total number of queries. On the one hand, we
describe simple active learning algorithms, which provably achieve an almost
optimal trade-off while giving cluster recovery guarantees, and we test them on
different datasets. On the other hand, we prove information-theoretical bounds
on the number of queries necessary to guarantee a prescribed disagreement
bound. These results give a rich characterization of the trade-off between
queries and clustering error
- …