31,343 research outputs found
Stable reduction of finite covers of curves
Let K be the function field of a connected regular scheme S of dimension 1,
and let f : X -> Y be a finite cover of projective smooth and geometrically
connected curves over K with g(X) greater or equal to 2. Suppose that f can be
extended to a finite cover {\mathcal X} -> {\mathcal Y} of semi-stable models
over S (it is known that this is always possible up to finite separable
extension of K). We prove that there then exists a (unique) minimal such cover.
This gives a canonical way to extend X -> Y to a finite cover of semi-stable
models over S.Comment: 19 pages, 2 figures. Minor changes. To appear in Compositio Mat
Distributed Learning in Multi-Armed Bandit with Multiple Players
We formulate and study a decentralized multi-armed bandit (MAB) problem.
There are M distributed players competing for N independent arms. Each arm,
when played, offers i.i.d. reward according to a distribution with an unknown
parameter. At each time, each player chooses one arm to play without exchanging
observations or any information with other players. Players choosing the same
arm collide, and, depending on the collision model, either no one receives
reward or the colliding players share the reward in an arbitrary way. We show
that the minimum system regret of the decentralized MAB grows with time at the
same logarithmic order as in the centralized counterpart where players act
collectively as a single entity by exchanging observations and making decisions
jointly. A decentralized policy is constructed to achieve this optimal order
while ensuring fairness among players and without assuming any pre-agreement or
information exchange among players. Based on a Time Division Fair Sharing
(TDFS) of the M best arms, the proposed policy is constructed and its order
optimality is proven under a general reward model. Furthermore, the basic
structure of the TDFS policy can be used with any order-optimal single-player
policy to achieve order optimality in the decentralized setting. We also
establish a lower bound on the system regret growth rate for a general class of
decentralized polices, to which the proposed policy belongs. This problem finds
potential applications in cognitive radio networks, multi-channel communication
systems, multi-agent systems, web search and advertising, and social networks.Comment: 31 pages, 8 figures, revised paper submitted to IEEE Transactions on
Signal Processing, April, 2010, the pre-agreement in the decentralized TDFS
policy is eliminated to achieve a complete decentralization among player
General Existence of Solutions to Dynamic Programming Principle
We provide an alternative approach to the existence of solutions to dynamic
programming equations arising in the discrete game-theoretic interpretations
for various nonlinear partial differential equations including the infinity
Laplacian, mean curvature flow and Hamilton-Jacobi type. Our general result is
similar to Perron's method but adapted to the discrete situation
Rational points of the group of components of a Neron model
Let A_K be an abelian variety over a discrete valuation field K. Let A be the
Neron model of A_K over the ring of integers O_K of K and A_k its special
fibre. We study the set of rational points of the group of components \phi_A of
A_k. In particular, we look at the cases where A_K is a Jacobian or where A_K
is an abelian variety having semi-stable reduction. We also consider algebraic
tori over K instead of abelian varieties.Comment: 16 page
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