We study the Chernoff-Stein exponent of the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the vector of inputs to the channel. Given the hypothesis, from the set associated with the hypothesis, an adversary chooses channels, one for each element of the input vector. Based on the channel outputs, a detector attempts to distinguish between the hypotheses. We study the Chernoff-Stein exponent for the cases where the transmitter (i) is deterministic, (ii) may privately randomize, and (iii) shares randomness with the detector that is unavailable to the adversary. It turns out that while a memoryless transmission strategy is optimal under shared randomness, it may be strictly suboptimal when the transmitter only has private randomness.

翻译：我们研究如下二元假设检验问题的Chernoff-Stein指数：每个假设关联一组信道。发送方在未知假设的情况下选择信道输入向量。在给定假设条件下，对抗者从该假设关联的信道集合中，为输入向量的每个元素分别选取一个信道。基于信道输出，检测器试图区分这两个假设。我们研究了发送方(i)采用确定性策略、(ii)允许私有随机化以及(iii)与检测器共享对抗者无法获取的随机性这三种情况下的Chernoff-Stein指数。结果表明，尽管在共享随机性条件下无记忆传输策略是最优的，但当发送方仅具有私有随机性时，该策略可能严格次优。