3,821 research outputs found
Game-theoretical control with continuous action sets
Motivated by the recent applications of game-theoretical learning techniques
to the design of distributed control systems, we study a class of control
problems that can be formulated as potential games with continuous action sets,
and we propose an actor-critic reinforcement learning algorithm that provably
converges to equilibrium in this class of problems. The method employed is to
analyse the learning process under study through a mean-field dynamical system
that evolves in an infinite-dimensional function space (the space of
probability distributions over the players' continuous controls). To do so, we
extend the theory of finite-dimensional two-timescale stochastic approximation
to an infinite-dimensional, Banach space setting, and we prove that the
continuous dynamics of the process converge to equilibrium in the case of
potential games. These results combine to give a provably-convergent learning
algorithm in which players do not need to keep track of the controls selected
by the other agents.Comment: 19 page
The impact of higher education for part-time students
This report discusses the findings of a study undertaken by Birkbeck, University of
London and the National Institute for Economic and Social Research, commissioned by
the UK Commission for Employment and Skills to examine the impact of higher education
(HE) on the labour market experiences of graduates who studied part-time and full-time
as undergraduates
Perturbative expansion of N<8 Supergravity
We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four
dimensions. For N=6 we find that the one-loop n-point amplitudes can be
expanded in terms of scalar box and triangle functions only. This
simplification is consistent with a loop momentum power count of n-3, which we
would interpret as being n+4 for gravity with a further -7 from the N=6
superalgebra. For N=4 we find that the amplitude is consistent with a loop
momentum power count of n, which we would interpret as being n+4 for gravity
with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes
contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt
1-loop N=4 SUGRA amplitude; v3 normalisations clarifie
Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
The decomposition of a one-loop scattering amplitude into elementary
functions with rational coefficients introduces spurious singularities which
afflict individual coefficients but cancel in the complete amplitude. These
cancellations create a web of interactions between the various terms. We
explore the extent to which entire one-loop amplitudes can be determined from
these relationships starting with a relatively small input of initial
information, typically the coefficients of the scalar integral functions as
these are readily determined. In the context of one-loop gravity amplitudes, of
which relatively little is known, we find that some amplitudes with a small
number of legs can be completely determined from their box coefficients. For
increasing numbers of legs, ambiguities appear which can be determined from the
physical singularity structure of the amplitude. We illustrate this with the
four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde
Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
We show how Supersymmetric Ward identities can be used to obtain amplitudes
involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain
results for all one-loop six-point NMHV amplitudes in \NeqFour Super
Yang-Mills theory which involve two gluinos or two scalar particles. More
general cases are also discussed.Comment: 32 pages, minor typos fixed; one reference adde
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