On the Fundamental Limitations of Decentralized Learnable Reward Shaping in Cooperative Multi-Agent Reinforcement Learning

Recent advances in learnable reward shaping have shown promise in single-agent reinforcement learning by automatically discovering effective feedback signals. However, the effectiveness of decentralized learnable reward shaping in cooperative multi-agent settings remains poorly understood. We propose DMARL-RSA, a fully decentralized system where each agent learns individual reward shaping, and evaluate it on cooperative navigation tasks in the simple_spread_v3 environment. Despite sophisticated reward learning, DMARL-RSA achieves only -24.20 +/- 0.09 average reward, compared to MAPPO with centralized training at 1.92 +/- 0.87 -- a 26.12-point gap. DMARL-RSA performs similarly to simple independent learning (IPPO: -23.19 +/- 0.96), indicating that advanced reward shaping cannot overcome fundamental decentralized coordination limitations. Interestingly, decentralized methods achieve higher landmark coverage (0.888 +/- 0.029 for DMARL-RSA, 0.960 +/- 0.045 for IPPO out of 3 total) but worse overall performance than centralized MAPPO (0.273 +/- 0.008 landmark coverage) -- revealing a coordination paradox between local optimization and global performance. Analysis identifies three critical barriers: (1) non-stationarity from concurrent policy updates, (2) exponential credit assignment complexity, and (3) misalignment between individual reward optimization and global objectives. These results establish empirical limits for decentralized reward learning and underscore the necessity of centralized coordination for effective multi-agent cooperation.