24,888 research outputs found
Epimorphisms of C*-algebras are surjective
We answer a question raised by V.G.Pestov in the affirmative.Comment: 2 page
Distribution-Free Learning
We select among rules for learning which of two actions in a stationary decision problem achieves a higher expected payo¤when payoffs realized by both actions are known in previous instances. Only a bounded set containing all possible payoffs is known. Rules are evaluated using maximum risk with maximin utility, minimax regret, competitive ratio and selection procedures being special cases. A randomized variant of fictitious play attains minimax risk for all risk functions with ex-ante expected payoffs increasing in the number of observations. Fictitious play itself has neither of these two properties. Tight bounds on maximal regret and probability of selecting the best action are included.fictitious play, nonparametric, finite sample, matched pairs, foregone payoffs, minimax risk, ex-ante improving, selection procedure
How to Attain Minimax Risk with Applications to Distribution-Free Nonparametric Estimation and Testing
We show how to a derive exact distribution-free nonparametric results for minimax risk when underlying random variables have known finite bounds and means are the only parameters of interest. Transform the data with a randomized mean preserving transformation into binary data and then apply the solution to minimax risk for the case where random variables are binary valued. This shows that minimax risk is attained by a linear strategy and the the set of binary valued distributions contains a least favorable prior. We apply these results to statistics. All unbiased symmetric non-randomized estimates for a function of the mean of a single sample are presented. We find a most powerful unbiased test for the mean of a single sample. We present tight lower bounds on size, type II error and minimal accuracy in terms of expected length of confidence intervals for a single mean and for the difference between two means. We show how to transform the randomized tests that attain the lower bounds into non-randomized tests that have at most twice the type I and II errors. Relative parameter efficiency can be measured in finite samples, in an example on anti-selfdealing indices relative (parameter) efficiency is 60% as compared to the tight lower bound. Our method can be used to generate distribution-free nonparametric estimates and tests when variance is the only parameter of interest. In particular we present a uniformly consistent estimator of standard deviation together with an upper bound on expected quadratic loss. We use our estimate to measure income inequality.exact, distribution-free, nonparametric inference, finite sample theory
Why Imitate, and if so, How? Exploring a Model of Social Evolution
In consectutive rounds, each agent in a finite population chooses an action, is randomly matched, obtains a payoff and then observes the performance of another agent. An agent determines future behavior based on the information she receives from the present round. She chooses among the behavioral rules that increase expected payoffs in any specifications of the matching scenario. The rule that outperforms all other such rules specifies to imitate the action of an agent that performed better with probability proportional to how much better she performed. The evolution of a large population in which each agent uses this rule can be approximated in the short run by the replicator dynamics.Random matching, learning, imitation, replicator dynamics
A Study of Truck Platooning Incentives Using a Congestion Game
We introduce an atomic congestion game with two types of agents, cars and
trucks, to model the traffic flow on a road over various time intervals of the
day. Cars maximize their utility by finding a trade-off between the time they
choose to use the road, the average velocity of the flow at that time, and the
dynamic congestion tax that they pay for using the road. In addition to these
terms, the trucks have an incentive for using the road at the same time as
their peers because they have platooning capabilities, which allow them to save
fuel. The dynamics and equilibria of this game-theoretic model for the
interaction between car traffic and truck platooning incentives are
investigated. We use traffic data from Stockholm to validate parts of the
modeling assumptions and extract reasonable parameters for the simulations. We
use joint strategy fictitious play and average strategy fictitious play to
learn a pure strategy Nash equilibrium of this game. We perform a comprehensive
simulation study to understand the influence of various factors, such as the
drivers' value of time and the percentage of the trucks that are equipped with
platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie
Dynamic surface critical behavior of isotropic Heisenberg ferromagnets: boundary conditions, renormalized field theory, and computer simulation results
The dynamic critical behavior of isotropic Heisenberg ferromagnets with a
planar free surface is investigated by means of field-theoretic renormalization
group techniques and high-precision computer simulations. An appropriate
semi-infinite extension of the stochastic model J is constructed. The relevant
boundary terms of the action of the associated dynamic field theory are
identified, the implied boundary conditions are derived, and the
renormalization of the model in bulk dimensions is clarified. Two
distinct renormalization schemes are utilized. The first is a massless one
based on minimal subtraction of dimensional poles and the dimensionality
expansion about . To overcome its problems in going below
dimensions, a massive one for fixed dimensions is constructed. The
resulting renormalization group (or Callan Symanzik) equations are exploited to
obtain the scaling forms of surface quantities like the dynamic structure
factor. In conjunction with boundary operator expansions scaling relations
follow that relate the critical indices of the dynamic and static infrared
singularities of surface quantities to familiar \emph{static} bulk and surface
exponents. To test the predicted scaling forms and scaling-law expressions for
the critical exponents involved, accurate computer-simulation data are
presented for the dynamic surface structure factor. These are in conformity
with our predictions.Comment: Revtex4-file with 4 figures included as eps-files, 21 pages in
print-format, typos corrected, to appear in Phys. Rev. B, July
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