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We investigate the problem of designing optimal stealthy poisoning attacks onthe control channel of Markov decision processes (MDPs). This research ismotivated by the recent interest of the research community for adversarial andpoisoning attacks applied to MDPs, and reinforcement learning (RL) methods. Thepolicies resulting from these methods have been shown to be vulnerable toattacks perturbing the observations of the decision-maker. In such an attack,drawing inspiration from adversarial examples used in supervised learning, theamplitude of the adversarial perturbation is limited according to some norm,with the hope that this constraint will make the attack imperceptible. However,such constraints do not grant any level of undetectability and do not take intoaccount the dynamic nature of the underlying Markov process. In this paper, wepropose a new attack formulation, based on information-theoretical quantities,that considers the objective of minimizing the detectability of the attack aswell as the performance of the controlled process. We analyze the trade-offbetween the efficiency of the attack and its detectability. We conclude withexamples and numerical simulations illustrating this trade-off.

Balancing detectability and performance of attacks on the control channel of Markov Decision Processes