A Theoretical and Empirical Analysis of Reward Transformations in Multi-Objective Stochastic Games

Reward shaping has been proposed as a means to address the credit assignment problem in Multi-Agent Systems (MAS). Two popular shaping methods are Potential-Based Reward Shaping and difference rewards, and both have been shown to improve learning speed and the quality of joint policies learned by agents in single-objective MAS. In this work we discuss the theoretical implications of applying these approaches to multi-objective MAS, and evaluate their efficacy using a new multi-objective benchmark domain where the true set of Pareto optimal system utilities is known.