169,442 research outputs found
An Approximate Subgame-Perfect Equilibrium Computation Technique for Repeated Games
This paper presents a technique for approximating, up to any precision, the
set of subgame-perfect equilibria (SPE) in discounted repeated games. The
process starts with a single hypercube approximation of the set of SPE. Then
the initial hypercube is gradually partitioned on to a set of smaller adjacent
hypercubes, while those hypercubes that cannot contain any point belonging to
the set of SPE are simultaneously withdrawn.
Whether a given hypercube can contain an equilibrium point is verified by an
appropriate mathematical program. Three different formulations of the algorithm
for both approximately computing the set of SPE payoffs and extracting players'
strategies are then proposed: the first two that do not assume the presence of
an external coordination between players, and the third one that assumes a
certain level of coordination during game play for convexifying the set of
continuation payoffs after any repeated game history.
A special attention is paid to the question of extracting players' strategies
and their representability in form of finite automata, an important feature for
artificial agent systems.Comment: 26 pages, 13 figures, 1 tabl
Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm
As an example of the recently-introduced concept of rate of innovation,
signals that are linear combinations of a finite number of Diracs per unit time
can be acquired by linear filtering followed by uniform sampling. However, in
reality, samples are rarely noiseless. In this paper, we introduce a novel
stochastic algorithm to reconstruct a signal with finite rate of innovation
from its noisy samples. Even though variants of this problem has been
approached previously, satisfactory solutions are only available for certain
classes of sampling kernels, for example kernels which satisfy the Strang-Fix
condition. In this paper, we consider the infinite-support Gaussian kernel,
which does not satisfy the Strang-Fix condition. Other classes of kernels can
be employed. Our algorithm is based on Gibbs sampling, a Markov chain Monte
Carlo (MCMC) method. Extensive numerical simulations demonstrate the accuracy
and robustness of our algorithm.Comment: Submitted to IEEE Transactions on Signal Processin
Importance sampling large deviations in nonequilibrium steady states. I
Large deviation functions contain information on the stability and response
of systems driven into nonequilibrium steady states, and in such a way are
similar to free energies for systems at equilibrium. As with equilibrium free
energies, evaluating large deviation functions numerically for all but the
simplest systems is difficult, because by construction they depend on
exponentially rare events. In this first paper of a series, we evaluate
different trajectory-based sampling methods capable of computing large
deviation functions of time integrated observables within nonequilibrium steady
states. We illustrate some convergence criteria and best practices using a
number of different models, including a biased Brownian walker, a driven
lattice gas, and a model of self-assembly. We show how two popular methods for
sampling trajectory ensembles, transition path sampling and diffusion Monte
Carlo, suffer from exponentially diverging correlations in trajectory space as
a function of the bias parameter when estimating large deviation functions.
Improving the efficiencies of these algorithms requires introducing guiding
functions for the trajectories.Comment: Published in JC
Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty
In this paper, we propose new sequential randomized algorithms for convex
optimization problems in the presence of uncertainty. A rigorous analysis of
the theoretical properties of the solutions obtained by these algorithms, for
full constraint satisfaction and partial constraint satisfaction, respectively,
is given. The proposed methods allow to enlarge the applicability of the
existing randomized methods to real-world applications involving a large number
of design variables. Since the proposed approach does not provide a priori
bounds on the sample complexity, extensive numerical simulations, dealing with
an application to hard-disk drive servo design, are provided. These simulations
testify the goodness of the proposed solution.Comment: 18 pages, Submitted for publication to IEEE Transactions on Automatic
Contro
Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
One of the key issues in the acquisition of sparse data by means of
compressed sensing (CS) is the design of the measurement matrix. Gaussian
matrices have been proven to be information-theoretically optimal in terms of
minimizing the required number of measurements for sparse recovery. In this
paper we provide a new approach for the analysis of the restricted isometry
constant (RIC) of finite dimensional Gaussian measurement matrices. The
proposed method relies on the exact distributions of the extreme eigenvalues
for Wishart matrices. First, we derive the probability that the restricted
isometry property is satisfied for a given sufficient recovery condition on the
RIC, and propose a probabilistic framework to study both the symmetric and
asymmetric RICs. Then, we analyze the recovery of compressible signals in noise
through the statistical characterization of stability and robustness. The
presented framework determines limits on various sparse recovery algorithms for
finite size problems. In particular, it provides a tight lower bound on the
maximum sparsity order of the acquired data allowing signal recovery with a
given target probability. Also, we derive simple approximations for the RICs
based on the Tracy-Widom distribution.Comment: 11 pages, 6 figures, accepted for publication in IEEE transactions on
information theor
Study of noise effects in electrical impedance tomography with resistor networks
We present a study of the numerical solution of the two dimensional
electrical impedance tomography problem, with noisy measurements of the
Dirichlet to Neumann map. The inversion uses parametrizations of the
conductivity on optimal grids. The grids are optimal in the sense that finite
volume discretizations on them give spectrally accurate approximations of the
Dirichlet to Neumann map. The approximations are Dirichlet to Neumann maps of
special resistor networks, that are uniquely recoverable from the measurements.
Inversion on optimal grids has been proposed and analyzed recently, but the
study of noise effects on the inversion has not been carried out. In this paper
we present a numerical study of both the linearized and the nonlinear inverse
problem. We take three different parametrizations of the unknown conductivity,
with the same number of degrees of freedom. We obtain that the parametrization
induced by the inversion on optimal grids is the most efficient of the three,
because it gives the smallest standard deviation of the maximum a posteriori
estimates of the conductivity, uniformly in the domain. For the nonlinear
problem we compute the mean and variance of the maximum a posteriori estimates
of the conductivity, on optimal grids. For small noise, we obtain that the
estimates are unbiased and their variance is very close to the optimal one,
given by the Cramer-Rao bound. For larger noise we use regularization and
quantify the trade-off between reducing the variance and introducing bias in
the solution. Both the full and partial measurement setups are considered.Comment: submitted to Inverse Problems and Imagin
Invaded cluster simulations of the XY model in two and three dimensions
The invaded cluster algorithm is used to study the XY model in two and three
dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model,
in the same universality class as the 3D XY model, is also studied. The static
critical properties of the model and the dynamical properties of the algorithm
are reported. The results are K_c=0.45412(2) for the 3D XY model and
eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results
are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show
any critical slowing for the magnetization or critical temperature estimator
for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v
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