Adversarial attacks during training can strongly influence the performance of multi-agent reinforcement learning algorithms. It is, thus, highly desirable to augment existing algorithms such that the impact of adversarial attacks on cooperative networks is eliminated, or at least bounded. In this work, we consider a fully decentralized network, where each agent receives a local reward and observes the global state and action. We propose a resilient consensus-based actor-critic algorithm, whereby each agent estimates the team-average reward and value function, and communicates the associated parameter vectors to its immediate neighbors. We show that in the presence of Byzantine agents, whose estimation and communication strategies are completely arbitrary, the estimates of the cooperative agents converge to a bounded consensus value with probability one, provided that there are at most $H$ Byzantine agents in the neighborhood of each cooperative agent and the network is $(2H+1)$-robust. Furthermore, we prove that the policy of the cooperative agents converges with probability one to a bounded neighborhood around a local maximizer of their team-average objective function under the assumption that the policies of the adversarial agents asymptotically become stationary.

翻译：培训期间的反方攻击可有力地影响多试剂强化学习算法的性能,因此,加强现有的算法是十分可取的,这样可以消除或至少消除对合作网络的对抗性攻击的影响。在这项工作中,我们考虑一个完全分散的网络,每个代理商都得到当地奖励并观察全球状况和行动。我们提出一个具有弹性的基于共识的行为体-批评算法,每个代理商都据此估计团队平均奖赏和价值功能,并将相关参数矢量传递给其近邻。我们表明,在拜占庭代理商(其估计和通信战略是完全武断的)在场的情况下,合作社代理商的估计接近一个受约束的共识值,概率为一,条件是每个合作代理商的邻里和网络的比占提纳代理人最多为(2H+1)美元-罗布特。此外,我们证明合作代理商的政策与其团队平均目标功能被捆绑在一起的邻居的概率一致。我们假设,即敌对代理人的政策会成为固定的固定。