246 research outputs found
Optimal Interdiction of Unreactive Markovian Evaders
The interdiction problem arises in a variety of areas including military
logistics, infectious disease control, and counter-terrorism. In the typical
formulation of network interdiction, the task of the interdictor is to find a
set of edges in a weighted network such that the removal of those edges would
maximally increase the cost to an evader of traveling on a path through the
network.
Our work is motivated by cases in which the evader has incomplete information
about the network or lacks planning time or computational power, e.g. when
authorities set up roadblocks to catch bank robbers, the criminals do not know
all the roadblock locations or the best path to use for their escape.
We introduce a model of network interdiction in which the motion of one or
more evaders is described by Markov processes and the evaders are assumed not
to react to interdiction decisions. The interdiction objective is to find an
edge set of size B, that maximizes the probability of capturing the evaders.
We prove that similar to the standard least-cost formulation for
deterministic motion this interdiction problem is also NP-hard. But unlike that
problem our interdiction problem is submodular and the optimal solution can be
approximated within 1-1/e using a greedy algorithm. Additionally, we exploit
submodularity through a priority evaluation strategy that eliminates the linear
complexity scaling in the number of network edges and speeds up the solution by
orders of magnitude. Taken together the results bring closer the goal of
finding realistic solutions to the interdiction problem on global-scale
networks.Comment: Accepted at the Sixth International Conference on integration of AI
and OR Techniques in Constraint Programming for Combinatorial Optimization
Problems (CPAIOR 2009
Informational Substitutes
We propose definitions of substitutes and complements for pieces of
information ("signals") in the context of a decision or optimization problem,
with game-theoretic and algorithmic applications. In a game-theoretic context,
substitutes capture diminishing marginal value of information to a rational
decision maker. We use the definitions to address the question of how and when
information is aggregated in prediction markets. Substitutes characterize
"best-possible" equilibria with immediate information aggregation, while
complements characterize "worst-possible", delayed aggregation. Game-theoretic
applications also include settings such as crowdsourcing contests and Q\&A
forums. In an algorithmic context, where substitutes capture diminishing
marginal improvement of information to an optimization problem, substitutes
imply efficient approximation algorithms for a very general class of (adaptive)
information acquisition problems.
In tandem with these broad applications, we examine the structure and design
of informational substitutes and complements. They have equivalent, intuitive
definitions from disparate perspectives: submodularity, geometry, and
information theory. We also consider the design of scoring rules or
optimization problems so as to encourage substitutability or complementarity,
with positive and negative results. Taken as a whole, the results give some
evidence that, in parallel with substitutable items, informational substitutes
play a natural conceptual and formal role in game theory and algorithms.Comment: Full version of FOCS 2016 paper. Single-column, 61 pages (48 main
text, 13 references and appendix
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
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