The majority of multi-agent reinforcement learning (MARL) implementations aim to optimize systems with respect to a single objective, despite the fact that many real-world problems are inherently multi-objective in nature. Research into multi-objective MARL is still in its infancy, and few studies to date have dealt with the issue of credit assignment. Reward shaping has been proposed as a means to address the credit assignment problem in single-objective MARL, however it has been shown to alter the intended goals of a domain if misused, leading to unintended behaviour. Two popular shaping methods are potential-based reward shaping and difference rewards, and both have been repeatedly shown to improve learning speed and the quality of joint policies learned by agents in single-objective MARL domains. This work discusses the theoretical implications of applying these shaping approaches to cooperative multi-objective MARL problems, and evaluates their efficacy using two benchmark domains. Our results constitute the first empirical evidence that agents using these shaping methodologies can sample true Pareto optimal solutions in cooperative multi-objective stochastic games.

Multi-agent systems (MASs) are a form of distributed intelligence, where multiple autonomous agents act in a common environment. Numerous complex, real world systems have been successfully optimized using multi-agent reinforcement learning (MARL) in conjunction with the MAS framework. In MARL agents learn by maximizing a scalar reward signal from the environment, and thus the design of the reward function directly affects the policies learned. In this work, we address the issue of appropriate multi-agent credit assignment in stochastic resource management games. We propose two new stochastic games to serve as testbeds for MARL research into resource management problems: the tragic commons domain and the shepherd problem domain. Our empirical work evaluates the performance of two commonly used reward shaping techniques: potential-based reward shaping and difference rewards. Experimental results demonstrate that systems using appropriate reward shaping techniques for multi-agent credit assignment can achieve near-optimal performance in stochastic resource management games, outperforming systems learning using unshaped local or global evaluations. We also present the first empirical investigations into the effect of expressing the same heuristic knowledge in state- or action-based formats, therefore developing insights into the design of multi-agent potential functions that will inform future work.