Shapley Q-value: A Local Reward Approach to Solve Global Reward Games
This addresses inefficiencies in learning for global reward games, which is a domain-specific problem in multi-agent systems.
The paper tackles the credit assignment problem in multi-agent reinforcement learning by proposing Shapley Q-value, a local reward approach that distributes global reward based on each agent's contribution, and demonstrates that their SQDDPG algorithm significantly improves convergence rates compared to state-of-the-art methods.
Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important problem studied in the global reward game. Most of previous works stood by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly. This, however, may give each agent an inaccurate reward on its contribution to the group, which could cause inefficient learning. To deal with this problem, we i) introduce a cooperative-game theoretical framework called extended convex game (ECG) that is a superset of global reward game, and ii) propose a local reward approach called Shapley Q-value. Shapley Q-value is able to distribute the global reward, reflecting each agent's own contribution in contrast to the shared reward approach. Moreover, we derive an MARL algorithm called Shapley Q-value deep deterministic policy gradient (SQDDPG), using Shapley Q-value as the critic for each agent. We evaluate SQDDPG on Cooperative Navigation, Prey-and-Predator and Traffic Junction, compared with the state-of-the-art algorithms, e.g., MADDPG, COMA, Independent DDPG and Independent A2C. In the experiments, SQDDPG shows a significant improvement on the convergence rate. Finally, we plot Shapley Q-value and validate the property of fair credit assignment.