This work considers a problem of integrated sensing and communication (ISAC) in which the goal of sensing is to detect a binary state. Unlike most approaches that minimize the total detection error probability, in our work, we disaggregate the error probability into false alarm and missed detection probabilities and investigate their information-theoretic three-way tradeoff including communication data rate. We consider a broadcast channel that consists of a transmitter, a communication receiver, and a detector where the receiver’s and the detector’s channels are affected by an unknown binary state. We consider and present results on two different state-dependent models. In the first setting, the state is fixed throughout the entire transmission, for which we fully characterize the optimal three-way tradeoff between the coding rate for communication and the two possibly nonidentical error exponents for sensing in the asymptotic regime. The achievability and converse proofs rely on the analysis of the cumulant-generating function of the log-likelihood ratio. In the second setting, the state changes every symbol in an independently and identically distributed (i.i.d.) manner, for which we characterize the optimal tradeoff region based on the analysis of the receiver operating characteristic (ROC) curves.

The concept of a minimax classifier is well-established in statistical decision theory, but its implementation via neural networks remains challenging, particularly in scenarios with imbalanced training data having a limited number of samples for minority classes. To address this issue, we propose a novel minimax learning algorithm designed to minimize the risk of worst-performing classes. Our algorithm iterates through two steps: a minimization step that trains the model based on a selected target prior, and a maximization step that updates the target prior towards the adversarial prior for the trained model. In the minimization, we introduce a targeted logit-adjustment loss function that efficiently identifies optimal decision boundaries under the target prior. Moreover, based on a new prior-dependent generalization bound that we obtained, we theoretically prove that our loss function has a better generalization capability than existing loss functions. During the maximization, we refine the target prior by shifting it towards the adversarial prior, depending on the worst-performing classes rather than on per-class risk estimates. Our maximization method is particularly robust in the regime of a small number of samples. Additionally, to adapt to overparameterized neural networks, we partition the entire training dataset into two subsets: one for model training during the minimization step and the other for updating the target prior during the maximization step. Our proposed algorithm has a provable convergence property, and empirical results indicate that our algorithm performs better than or is comparable to existing methods.