174,635 research outputs found
Improvements on the k-center problem for uncertain data
In real applications, there are situations where we need to model some
problems based on uncertain data. This leads us to define an uncertain model
for some classical geometric optimization problems and propose algorithms to
solve them. In this paper, we study the -center problem, for uncertain
input. In our setting, each uncertain point is located independently from
other points in one of several possible locations in a metric space with metric , with specified probabilities
and the goal is to compute -centers that minimize the
following expected cost here
is the probability space of all realizations of given uncertain points and
In restricted assigned version of this problem, an assignment is given for any choice of centers and the
goal is to minimize In unrestricted version, the
assignment is not specified and the goal is to compute centers
and an assignment that minimize the above expected
cost.
We give several improved constant approximation factor algorithms for the
assigned versions of this problem in a Euclidean space and in a general metric
space. Our results significantly improve the results of \cite{guh} and
generalize the results of \cite{wang} to any dimension. Our approach is to
replace a certain center point for each uncertain point and study the
properties of these certain points. The proposed algorithms are efficient and
simple to implement
The Stellar-Dynamical Search for Supermassive Black Holes in Galactic Nuclei
The robustness of stellar-dynamical black hole (BH) mass measurements is
illustrated using 7 galaxies that have results from independent groups. Derived
masses have remained constant to a factor of about 2 as spatial resolution has
improved by factors of 2 - 330 and as the analysis has improved from spherical,
isotropic models to axisymmetric, three-integral models. This gives us
confidence that the masses are reliable and that the galaxies do not indulge in
a wide variety of perverse orbital structures. Constraints on BH alternatives
are also improving. In M31, Hubble Space Telescope (HST) spectroscopy shows
that the central massive dark object (MDO) is in a tiny cluster of blue stars
embedded in the P2 nucleus of the galaxy. The MDO must be less than about 0.06
arcsec in radius. M31 becomes the third galaxy in which dark clusters of brown
dwarf stars or stellar remnants can be excluded. In our Galaxy, observations of
almost-complete stellar orbits show that the MDO radius is less than about
0.0006 pc. Among BH alternatives, this excludes even neutrino balls. Therefore,
measurements of central dark masses and the conclusion that these are BHs have
both stood the test of time. Confidence in the BH paradigm for active galactic
nuclei is correspondingly high. Compared to the radius of the BH sphere of
influence, BHs are discovered at similar spatial resolution with HST as in
ground-based work. The reason is that HST is used to observe more distant
galaxies. Large, unbiased samples are accessible. As a result, HST has
revolutionized the study of BH demographics.Comment: 20 pages, 5 figures + 2 tables embedded as figures, LaTeX2e with
wrapping fixed, uses ociwsymp1.sty; To appear in "Carnegie Observatories
Astrophysics Series, Vol. 1: Coevolution of Black Holes and Galaxies," ed. L.
C. Ho (Cambridge: Cambridge Univ. Press
Using Monte Carlo Search With Data Aggregation to Improve Robot Soccer Policies
RoboCup soccer competitions are considered among the most challenging
multi-robot adversarial environments, due to their high dynamism and the
partial observability of the environment. In this paper we introduce a method
based on a combination of Monte Carlo search and data aggregation (MCSDA) to
adapt discrete-action soccer policies for a defender robot to the strategy of
the opponent team. By exploiting a simple representation of the domain, a
supervised learning algorithm is trained over an initial collection of data
consisting of several simulations of human expert policies. Monte Carlo policy
rollouts are then generated and aggregated to previous data to improve the
learned policy over multiple epochs and games. The proposed approach has been
extensively tested both on a soccer-dedicated simulator and on real robots.
Using this method, our learning robot soccer team achieves an improvement in
ball interceptions, as well as a reduction in the number of opponents' goals.
Together with a better performance, an overall more efficient positioning of
the whole team within the field is achieved
Safe Approximations of Chance Constraints Using Historical Data
This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical-data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.robust optimization;chance constraint;phi-divergence;goodness-of-fit statistics
Learning relational dynamics of stochastic domains for planning
Probabilistic planners are very flexible tools that can provide good solutions for difficult tasks. However, they rely on a model of the domain, which may be costly to either hand code or automatically learn for complex tasks. We propose a new learning approach that (a) requires only a set of state transitions to learn the model; (b) can cope with uncertainty in the effects; (c) uses a relational representation to generalize over different objects; and (d) in addition to action effects, it can also learn exogenous effects that are not related to any action, e.g., moving objects, endogenous growth and natural development. The proposed learning approach combines a multi-valued variant of inductive logic programming for the generation of candidate models, with an optimization method to select the best set of planning operators to model a problem. Finally, experimental validation is provided that shows improvements over previous work.Peer ReviewedPostprint (author's final draft
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