We analyze a distributed stochastic bandit model in which an agent controls multiple independent stochastic bandit machines. At each time step, the agent selects several machines for parallel exploitation but the arm pulled by each machine may differ from the command received either randomly (defective command) or adversarially (corrupted command). Machines that faithfully execute commands are called honest. We study situations in which the number of honest machines is either known or unknown and define appropriate notions of regret. With at least one honest machine and a known number of honest bandits, we provide a simple algorithm that achieves $\tilde O\left( {{n^{1/2}}} \right)$ regrets when commands are corrupted. Lower bounds on regret established by drawing connections to the problem of "low probability of detection," show the near optimality of the regret achieved by the algorithms.

We consider a communication model in which a transmitter attempts to communicate with a receiver over a state-dependent channel and simultaneously estimates the state using strictly causal noisy state observations. The state is assumed to remain constant over the duration of the transmission. We analyze the trade-off between the state-error exponent and the communication rate in the sequential setting, in which the transmitter determines what and how many symbols to transmit in an online manner.

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.

We consider the problem of authenticating communication over a Myopic Binary Adversarial Channel (MBAC) while maintaining covertness with respect to the myopic adversary. When the main channel between legitimate parties is degraded with respect to the adversary's channel, we show the existence of an integrated scheme that simultaneously exploits secret keys to ensure covertness and authentication. The main technical challenge we address is showing that authentication may be ensured against myopic attacks when using the low-weight codewords mandated by covert communication.

We consider the problem of covert sequential testing, in which a legitimate party attempts to run a sequential test while escaping detection from an adversary. Specifically, the legitimate party’s decisions should meet prescribed risk constraints and, simultaneously, the adversary’s observations induced by the test should remain indistinguishable from the observations obtained in the absence of a test. Our main result is the characterization of the risk exponent ${\gamma}_{{\theta}}$, which captures the asymptotic exponential decrease of the risk with the square-root of the averaged stopping time in the limit of low risk. An example is provided to illustrate how the covertness constraint influences the design of the sequential test.

We consider an active hypothesis testing scenario in which an adversary obtains observations while legitimate parties engage in a sequential adaptive control policy to estimate an unknown parameter. The objective is for the legitimate parties to evade the adversary by controlling the risk of their test while minimizing the detection ability of the adversary, measured in terms of its error exponent. We develop bounds on the adversary's error exponent that offer insight into how legitimate adversaries can best evade the adversary's detection. We illustrate the results in a wireless transmission detection example.