The fundamental problem of multiple secondary users contending for
opportunistic spectrum access over multiple channels in cognitive radio
networks has been formulated recently as a decentralized multi-armed bandit
(D-MAB) problem. In a D-MAB problem there are $M$ users and $N$ arms (channels)
that each offer i.i.d. stochastic rewards with unknown means so long as they
are accessed without collision. The goal is to design a decentralized online
learning policy that incurs minimal regret, defined as the difference between
the total expected rewards accumulated by a model-aware genie, and that
obtained by all users applying the policy. We make two contributions in this
paper. First, we consider the setting where the users have a prioritized
ranking, such that it is desired for the $K$-th-ranked user to learn to access
the arm offering the $K$-th highest mean reward. For this problem, we present
the first distributed policy that yields regret that is uniformly logarithmic
over time without requiring any prior assumption about the mean rewards.
Second, we consider the case when a fair access policy is required, i.e., it is
desired for all users to experience the same mean reward. For this problem, we
present a distributed policy that yields order-optimal regret scaling with
respect to the number of users and arms, better than previously proposed
policies in the literature. Both of our distributed policies make use of an
innovative modification of the well known UCB1 policy for the classic
multi-armed bandit problem that allows a single user to learn how to play the
arm that yields the $K$-th largest mean reward.

本文针对认知无线电网络中的多个次级用户争取多个信道的机会问题，提出去中心化多臂赌博问题，并设计出一种去中心化的在线学习策略，以达到尽可能降低总体期望回报与所有用户回归之间的差距。其中，分别考虑了优先级排序和公平访问策略。