Cooperative Multi-Agent Reinforcement Learning (MARL) algorithms, trained only to optimize task reward, can lead to a concentration of power where the failure or adversarial intent of a single agent could decimate the reward of every agent in the system. In the context of teams of people, it is often useful to explicitly consider how power is distributed to ensure no person becomes a single point of failure. Here, we argue that explicitly regularizing the concentration of power in cooperative RL systems can result in systems which are more robust to single agent failure, adversarial attacks, and incentive changes of co-players. To this end, we define a practical pairwise measure of power that captures the ability of any co-player to influence the ego agent's reward, and then propose a power-regularized objective which balances task reward and power concentration. Given this new objective, we show that there always exists an equilibrium where every agent is playing a power-regularized best-response balancing power and task reward. Moreover, we present two algorithms for training agents towards this power-regularized objective: Sample Based Power Regularization (SBPR), which injects adversarial data during training; and Power Regularization via Intrinsic Motivation (PRIM), which adds an intrinsic motivation to regulate power to the training objective. Our experiments demonstrate that both algorithms successfully balance task reward and power, leading to lower power behavior than the baseline of task-only reward and avoid catastrophic events in case an agent in the system goes off-policy.

Communication plays a vital role for coordination in Multi-Agent Reinforcement Learning (MARL) systems. However, misaligned agents can exploit other agents' trust and delegated power to the communication medium. In this paper, we propose power regularization as a method to limit the adverse effects of communication by misaligned agents, specifically communication which impairs the performance of cooperative agents. Power is a measure of the influence one agent's actions have over another agent's policy. By introducing power regularization, we aim to allow designers to control or reduce agents' dependency on communication when appropriate, and make them more resilient to performance deterioration due to misuses of communication. We investigate several environments in which power regularization can be a valuable capability for learning different policies that reduce the effect of power dynamics between agents during communication.