Optimizing decision fusion in the presence of Byzantine data

We consider the problem of fusing local decision outputs into a global decision with a budget constraint in the presence of Byzantine data. Each local decision maker is assumed to provide finite output regarding two competing hypotheses. A fusion rule is characterized by probabilistic mixing of decision trees corresponding to deterministic policies to reach a global decision. For practical problems where maximizing detection probability is of primary concern, we propose to optimize the fusion rule under the budget constraint so that the fusion center can maintain the expected operational cost in the long run. In addition, we assume that each local processor receives the feedback from the fusion center sequentially in order to achieve the desired false alarm rate. A practical procedure based on the conformal prediction method is proposed for the honest local processor to adapt to the globally optimal decision fusion policy against Byzantine attack. We show that the attacker can only reduce the detection probability vs. budget curve to the situation where the fusion center has full knowledge of the compromised local processors in the asymptotic regime. Illustrative examples regarding the conflict detection problem in air traffic management are provided for policy analysis within the optimization of the decision fusion in the presence of Byzantine data.