30,175 research outputs found
Reconfiguration in bounded bandwidth and treedepth
We show that several reconfiguration problems known to be PSPACE-complete
remain so even when limited to graphs of bounded bandwidth. The essential step
is noticing the similarity to very limited string rewriting systems, whose
ability to directly simulate Turing Machines is classically known. This
resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show
that a large class of reconfiguration problems becomes tractable on graphs of
bounded treedepth, and that this result is in some sense tight.Comment: 14 page
Weakly Admissible Vector Equilibrium Problems
We establish lower semi-continuity and strict convexity of the energy
functionals for a large class of vector equilibrium problems in logarithmic
potential theory. This in particular implies the existence and uniqueness of a
minimizer for such vector equilibrium problems. Our work extends earlier
results in that we allow unbounded supports without having strongly confining
external fields. To deal with the possible noncompactness of supports, we map
the vector equilibrium problem onto the Riemann sphere and our results follow
from a study of vector equilibrium problems on compacts in higher dimensions.
Our results cover a number of cases that were recently considered in random
matrix theory and for which the existence of a minimizer was not clearly
established yet.Comment: 16 page
Path Planning Problems with Side Observations-When Colonels Play Hide-and-Seek
Resource allocation games such as the famous Colonel Blotto (CB) and
Hide-and-Seek (HS) games are often used to model a large variety of practical
problems, but only in their one-shot versions. Indeed, due to their extremely
large strategy space, it remains an open question how one can efficiently learn
in these games. In this work, we show that the online CB and HS games can be
cast as path planning problems with side-observations (SOPPP): at each stage, a
learner chooses a path on a directed acyclic graph and suffers the sum of
losses that are adversarially assigned to the corresponding edges; and she then
receives semi-bandit feedback with side-observations (i.e., she observes the
losses on the chosen edges plus some others). We propose a novel algorithm,
EXP3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP
without requiring any auxiliary oracle. We provide an expected-regret bound of
EXP3-OE in SOPPP matching the order of the best benchmark in the literature.
Moreover, we introduce additional assumptions on the observability model under
which we can further improve the regret bounds of EXP3-OE. We illustrate the
benefit of using EXP3-OE in SOPPP by applying it to the online CB and HS games.Comment: Previously, this work appeared as arXiv:1911.09023 which was
mistakenly submitted as a new article (has been submitted to be withdrawn).
This is a preprint of the work published in Proceedings of the 34th AAAI
Conference on Artificial Intelligence (AAAI
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