The challenge of hidden gifts in multi-agent reinforcement learning

Sometimes we benefit from actions that others have taken even when we are unaware that they took those actions. For example, if your neighbor chooses not to take a parking spot in front of your house when you are not there, you can benefit, even without being aware that they took this action. These ``hidden gifts'' represent an interesting challenge for multi-agent reinforcement learning (MARL), since assigning credit when the beneficial actions of others are hidden is non-trivial. Here, we study the impact of hidden gifts with a simple MARL task. In this task, agents in a grid-world environment have individual doors to unlock in order to obtain individual rewards. As well, if all the agents unlock their door the group receives a larger collective reward. However, there is only one key for all of the doors, such that the collective reward can only be obtained when the agents drop the key for others after they use it. Notably, there is nothing to indicate to an agent that the other agents have dropped the key, thus this act for others is a ``hidden gift''. We show that several different state-of-the-art MARL algorithms, including MARL specific architectures, fail to learn how to obtain the collective reward in this simple task. Interestingly, we find that decentralized actor-critic policy gradient agents can succeed when we provide them with information about their own action history, but MARL agents still cannot solve the task with action history. Finally, we derive a correction term for policy gradient agents, inspired by learning aware approaches, which reduces the variance in learning and helps them to converge to collective success more reliably. These results show that credit assignment in multi-agent settings can be particularly challenging in the presence of ``hidden gifts'', and demonstrate that self learning-awareness in decentralized agents can benefit these settings.