  Finding optimal adversarial attack strategies is an important topic in
reinforcement learning and the Markov decision process. Previous studies
usually assume one all-knowing coordinator (attacker) for whom attacking
different recipient (victim) agents incurs uniform costs. However, in reality,
instead of using one limitless central attacker, the attacks often need to be
performed by distributed attack agents. We formulate the problem of performing
optimal adversarial agent-to-agent attacks using distributed attack agents, in
which we impose distinct cost constraints on each different attacker-victim
pair. We propose an optimal method integrating within-step static constrained
attack-resource allocation optimization and between-step dynamic programming to
achieve the optimal adversarial attack in a multi-agent system. Our numerical
results show that the proposed attacks can significantly reduce the rewards
received by the attacked agents.
