The problem of identifying the channel with the highest capacity among several discrete memoryless channels (DMCs) is considered. The problem is cast as a pure-exploration multi-armed bandit problem, which follows the practical use of training sequences to sense the communication channel statistics. A capacity estimator is proposed and tight confidence bounds on the estimator error are derived. Based on this capacity estimator, a gap-elimination algorithm termed BestChanID is proposed, which is oblivious to the capacity-achieving input distribution and is guaranteed to output the DMC with the largest capacity, with a desired confidence. Furthermore, two additional algorithms NaiveChanSel and MedianChanEl, that output with certain confidence a DMC with capacity close to the maximal, are introduced. Each of those algorithms is beneficial in a different regime and can be used as a subroutine in BestChanID. The sample complexity of all algorithms is analyzed as a function of the desired confidence parameter, the number of channels, and the channels' input and output alphabet sizes. The cost of best channel identification is shown to scale quadratically with the alphabet size, and a fundamental lower bound for the required number of channel senses to identify the best channel with a certain confidence is derived.

翻译：本文研究了在多个离散无记忆信道（DMC）中识别具有最高容量的信道问题。将该问题转化为纯探索型多臂赌博机问题，其遵循利用训练序列感知通信信道统计特性的实际应用。提出了一种容量估计器，并推导出该估计误差的紧致置信界。基于该容量估计器，提出了一种名为BestChanID的间隙消除算法，该算法对容量可达输入分布具有无偏性，并能以期望置信度保证输出具有最大容量的DMC。此外，还引入了两种额外算法NaiveChanSel和MedianChanEl，它们能以一定置信度输出容量接近最大值的DMC。每种算法在不同场景下具有优势，并可作为BestChanID的子程序使用。所有算法的样本复杂度被分析为期望置信度参数、信道数量以及信道输入输出字母表大小的函数。最优信道识别的代价被证明随字母表大小呈二次方增长，并推导出以特定置信度识别最优信道所需的最少信道感知次数的理论下界。