8,442 research outputs found
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
The market for protection and the origin of the state
We examine a stark setting in which security or protection can be provided by self-governing groups or by for-profit entrepreneurs (kings, kleptocrats, or mafia dons). Though selfgovernance is best for the population, it faces problems of long-term viability. Typically, in providing security the equilibrium market structure involves competing lords, a condition that leads to a tragedy of coercion: all the savings from the provision of collective protection are dissipated and welfare can be as low as, or even lower than, in the absence of the state
Generalized models as a universal approach to the analysis of nonlinear dynamical systems
We present a universal approach to the investigation of the dynamics in
generalized models. In these models the processes that are taken into account
are not restricted to specific functional forms. Therefore a single generalized
models can describe a class of systems which share a similar structure. Despite
this generality, the proposed approach allows us to study the dynamical
properties of generalized models efficiently in the framework of local
bifurcation theory. The approach is based on a normalization procedure that is
used to identify natural parameters of the system. The Jacobian in a steady
state is then derived as a function of these parameters. The analytical
computation of local bifurcations using computer algebra reveals conditions for
the local asymptotic stability of steady states and provides certain insights
on the global dynamics of the system. The proposed approach yields a close
connection between modelling and nonlinear dynamics. We illustrate the
investigation of generalized models by considering examples from three
different disciplines of science: a socio-economic model of dynastic cycles in
china, a model for a coupled laser system and a general ecological food web.Comment: 15 pages, 2 figures, (Fig. 2 in color
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