Hybrid Differential Reward: Combining Temporal Difference and Action Gradients for Efficient Multi-Agent Reinforcement Learning in Cooperative Driving

In multi-vehicle cooperative driving tasks involving high-frequency continuous control, traditional state-based reward functions suffer from the issue of vanishing reward differences. This phenomenon results in a low signal-to-noise ratio (SNR) for policy gradients, significantly hindering algorithm convergence and performance improvement. To address this challenge, this paper proposes a novel Hybrid Differential Reward (HDR) mechanism. We first theoretically elucidate how the temporal quasi-steady nature of traffic states and the physical proximity of actions lead to the failure of traditional reward signals. Building on this analysis, the HDR framework innovatively integrates two complementary components: (1) a Temporal Difference Reward (TRD) based on a global potential function, which utilizes the evolutionary trend of potential energy to ensure optimal policy invariance and consistency with long-term objectives; and (2) an Action Gradient Reward (ARG), which directly measures the marginal utility of actions to provide a local guidance signal with a high SNR. Furthermore, we formulate the cooperative driving problem as a Multi-Agent Partially Observable Markov Game (POMDPG) with a time-varying agent set and provide a complete instantiation scheme for HDR within this framework. Extensive experiments conducted using both online planning (MCTS) and Multi-Agent Reinforcement Learning (QMIX, MAPPO, MADDPG) algorithms demonstrate that the HDR mechanism significantly improves convergence speed and policy stability. The results confirm that HDR guides agents to learn high-quality cooperative policies that effectively balance traffic efficiency and safety.