Connected Autonomous Vehicles (CAVs) promise to reduce congestion in future urban networks, potentially by optimizing their routing decisions. Unlike for human drivers, these decisions can be made with collective, data-driven policies, developed using machine learning algorithms. Reinforcement learning (RL) can facilitate the development of such collective routing strategies, yet standardized and realistic benchmarks are missing.

In cooperative Multi-Agent Reinforcement Learning (MARL), agents that share policy network parameters often learn similar behaviors, which hinders effective exploration and can lead to suboptimal cooperative policies. Recent advances have attempted to promote multi-agent diversity by leveraging the Wasserstein distance to increase policy differences. However, these methods cannot effectively encourage diverse policies due to ineffective Wasserstein distance caused by the policy similarity. To address this limitation, we propose Wasserstein Contrastive Diversity (WCD) exploration, a novel approach that promotes multi-agent diversity by maximizing the Wasserstein distance between the trajectory distributions of different agents in a latent representation space. To make the Wasserstein distance meaningful, we propose a novel next-step prediction method based on Contrastive Predictive Coding (CPC) to learn distinguishable trajectory representations. Additionally, we introduce an optimized kernel-based method to compute the Wasserstein distance more efficiently. Since the Wasserstein distance is inherently defined for two distributions, we extend it to support multiple agents, enabling diverse policy learning. Empirical evaluations across a variety of challenging multi-agent tasks demonstrate that WCD outperforms existing state-of-the-art methods, delivering superior performance and enhanced exploration.

In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. In this work, we provide a unified framework that connects noise contrastive estimation (NCE), reverse logistic regression (RLR), multiple importance sampling (MIS), and bridge sampling within the context of EBMs. We further show that these methods are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Hence, rather than being a purely descriptive review, this work offers a unifying perspective and additional methodological contributions. The MATLAB code used in the numerical experiments is also made freely available to support the reproducibility of the results.

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We thank all the reviewers for their feedback. All reviewers are concerned whether we substantially outperform QMIX. Since StarCraft II experiments take a long time, we could not include all the results in the submission. Samvelyan et al. have classified as Easy, Hard & Super Hard. Results on several maps are shown below.