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We consider a non-adaptive controlled sensing sce-nario in which the actions of the decision maker are corrupted by an adversary. The objective of the decision maker is to either detect the presence of the corruption or make a correct decision. Accordingly, the performance of a controlled sensing strategy is measured in terms of the error probability when there is no adversary, denoted PE,0 , and the error probability when an adversary is present, denoted PE,1 . Our main result is Stein-lemma like characterization of the optimal achievable error exponent of PE,0 subject to a constraint on PE,1 . We also illustrate the result with numerical examples.more » « less
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We study the covert best arm identification problem in which an agent tries to identify the best arm while escaping detection from an adversary. Specifically, the agent should identify the best arm of the bandit with accuracy higher than a predefined requirement as soon as possible and, simultaneously, the adversary’s observations induced by pulling effective arms should remain indistinguishable from the observations obtained when no effective arm is pulled. Our main result is the characterization of the exponent γ, which captures the asymptotic exponential decrease of the confidence level with the square-root of the averaged stopping time.more » « less
