201 research outputs found
Migration as Submodular Optimization
Migration presents sweeping societal challenges that have recently attracted
significant attention from the scientific community. One of the prominent
approaches that have been suggested employs optimization and machine learning
to match migrants to localities in a way that maximizes the expected number of
migrants who find employment. However, it relies on a strong additivity
assumption that, we argue, does not hold in practice, due to competition
effects; we propose to enhance the data-driven approach by explicitly
optimizing for these effects. Specifically, we cast our problem as the
maximization of an approximately submodular function subject to matroid
constraints, and prove that the worst-case guarantees given by the classic
greedy algorithm extend to this setting. We then present three different models
for competition effects, and show that they all give rise to submodular
objectives. Finally, we demonstrate via simulations that our approach leads to
significant gains across the board.Comment: Simulation code is available at https://github.com/pgoelz/migration
A Smooth Transition from Powerlessness to Absolute Power
We study the phase transition of the coalitional manipulation problem for
generalized scoring rules. Previously it has been shown that, under some
conditions on the distribution of votes, if the number of manipulators is
, where is the number of voters, then the probability that a
random profile is manipulable by the coalition goes to zero as the number of
voters goes to infinity, whereas if the number of manipulators is
, then the probability that a random profile is manipulable
goes to one. Here we consider the critical window, where a coalition has size
, and we show that as goes from zero to infinity, the limiting
probability that a random profile is manipulable goes from zero to one in a
smooth fashion, i.e., there is a smooth phase transition between the two
regimes. This result analytically validates recent empirical results, and
suggests that deciding the coalitional manipulation problem may be of limited
computational hardness in practice.Comment: 22 pages; v2 contains minor changes and corrections; v3 contains
minor changes after comments of reviewer
Learning Cooperative Games
This paper explores a PAC (probably approximately correct) learning model in
cooperative games. Specifically, we are given random samples of coalitions
and their values, taken from some unknown cooperative game; can we predict the
values of unseen coalitions? We study the PAC learnability of several
well-known classes of cooperative games, such as network flow games, threshold
task games, and induced subgraph games. We also establish a novel connection
between PAC learnability and core stability: for games that are efficiently
learnable, it is possible to find payoff divisions that are likely to be stable
using a polynomial number of samples.Comment: accepted to IJCAI 201
Computation-Aware Data Aggregation
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes\u27 input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do not take compute time into account. Rather, most distributed models of computation only explicitly consider communication time.
In this paper, we introduce a model of distributed computation that considers both computation and communication so as to give a theoretical treatment of data aggregation. We study both the structure of and how to compute the fastest data aggregation schedule in this model. As our first result, we give a polynomial-time algorithm that computes the optimal schedule when the input network is a complete graph. Moreover, since one may want to aggregate data over a pre-existing network, we also study data aggregation scheduling on arbitrary graphs. We demonstrate that this problem on arbitrary graphs is hard to approximate within a multiplicative 1.5 factor. Finally, we give an O(log n ? log(OPT/t_m))-approximation algorithm for this problem on arbitrary graphs, where n is the number of nodes and OPT is the length of the optimal schedule
An Algorithmic Framework for Strategic Fair Division
We study the paradigmatic fair division problem of allocating a divisible
good among agents with heterogeneous preferences, commonly known as cake
cutting. Classical cake cutting protocols are susceptible to manipulation. Do
their strategic outcomes still guarantee fairness?
To address this question we adopt a novel algorithmic approach, by designing
a concrete computational framework for fair division---the class of Generalized
Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic
properties of algorithms that operate in this model. The class of GCC protocols
includes the most important discrete cake cutting protocols, and turns out to
be compatible with the study of fair division among strategic agents. In
particular, GCC protocols are guaranteed to have approximate subgame perfect
Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule
is flexible. We further observe that the (approximate) equilibria of
proportional GCC protocols---which guarantee each of the agents a
-fraction of the cake---must be (approximately) proportional. Finally, we
design a protocol in this framework with the property that its Nash equilibrium
allocations coincide with the set of (contiguous) envy-free allocations
Influence in Classification via Cooperative Game Theory
A dataset has been classified by some unknown classifier into two types of
points. What were the most important factors in determining the classification
outcome? In this work, we employ an axiomatic approach in order to uniquely
characterize an influence measure: a function that, given a set of classified
points, outputs a value for each feature corresponding to its influence in
determining the classification outcome. We show that our influence measure
takes on an intuitive form when the unknown classifier is linear. Finally, we
employ our influence measure in order to analyze the effects of user profiling
on Google's online display advertising.Comment: accepted to IJCAI 201
Sum of Us: Strategyproof Selection from the Selectors
We consider directed graphs over a set of n agents, where an edge (i,j) is
taken to mean that agent i supports or trusts agent j. Given such a graph and
an integer k\leq n, we wish to select a subset of k agents that maximizes the
sum of indegrees, i.e., a subset of k most popular or most trusted agents. At
the same time we assume that each individual agent is only interested in being
selected, and may misreport its outgoing edges to this end. This problem
formulation captures realistic scenarios where agents choose among themselves,
which can be found in the context of Internet search, social networks like
Twitter, or reputation systems like Epinions.
Our goal is to design mechanisms without payments that map each graph to a
k-subset of agents to be selected and satisfy the following two constraints:
strategyproofness, i.e., agents cannot benefit from misreporting their outgoing
edges, and approximate optimality, i.e., the sum of indegrees of the selected
subset of agents is always close to optimal. Our first main result is a
surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof
mechanism can provide a finite approximation ratio. Our second main result is a
randomized strategyproof mechanism with an approximation ratio that is bounded
from above by four for any value of k, and approaches one as k grows
- …