Bi-level Mean Field: Dynamic Grouping for Large-Scale MARL (2505.06706v2)

Abstract: Large-scale Multi-Agent Reinforcement Learning (MARL) often suffers from the curse of dimensionality, as the exponential growth in agent interactions significantly increases computational complexity and impedes learning efficiency. To mitigate this, existing efforts that rely on Mean Field (MF) simplify the interaction landscape by approximating neighboring agents as a single mean agent, thus reducing overall complexity to pairwise interactions. However, these MF methods inevitably fail to account for individual differences, leading to aggregation noise caused by inaccurate iterative updates during MF learning. In this paper, we propose a Bi-level Mean Field (BMF) method to capture agent diversity with dynamic grouping in large-scale MARL, which can alleviate aggregation noise via bi-level interaction. Specifically, BMF introduces a dynamic group assignment module, which employs a Variational AutoEncoder (VAE) to learn the representations of agents, facilitating their dynamic grouping over time. Furthermore, we propose a bi-level interaction module to model both inter- and intra-group interactions for effective neighboring aggregation. Experiments across various tasks demonstrate that the proposed BMF yields results superior to the state-of-the-art methods.

Bi-level Mean Field: Dynamic Grouping for Large-Scale MARL

In the domain of multi-agent systems, scaling reinforcement learning (RL) to handle large groups of interacting agents presents significant challenges, primarily due to the curse of dimensionality. Existing approaches often resort to mean field (MF) approximations to simplify the interaction complexity by averaging the influence of neighboring agents into a single virtual agent. This method substantially reduces computational demands but at the cost of disregarding individual agent characteristics, introducing aggregation noise and impeding learning accuracy.

The paper "Bi-level Mean Field: Dynamic Grouping for Large-Scale MARL" proposes an innovative Bi-level Mean Field (BMF) method to address these limitations by incorporating agent diversity through dynamic grouping. This approach not only captures the heterogeneity of agents but also mitigates the aggregation noise inherent in traditional MF methods, enhancing performance in large-scale multi-agent reinforcement learning (MARL) environments.

Key Contributions and Methodology

Dynamic Group Assignment:

A dynamic group assignment module is introduced, employing a Variational AutoEncoder (VAE) to extract agent features based on their observations and actions. These features facilitate the adaptive grouping of agents into clusters over time using k-means clustering. This dynamic approach enables BMF to adapt to various agent interactions without prior knowledge of agent types.

Bi-level Interaction Module:

The novel two-level interaction framework distinguishes between intra-group and inter-group interactions. Intra-group interactions use unweighted MF methods, attributing homogeneous behaviors to agents within the same group. Conversely, inter-group interactions leverage a group attention mechanism to model the dynamics between heterogeneous agents across groups, offering a more nuanced approximation than conventional MF.

Theoretical Analysis and Experimental Validation

The paper provides a theoretical foundation for BMF, asserting that under certain conditions, the global Q-function approximated by BMF accurately accounts for both intra-group and inter-group interactions. Furthermore, the error analysis confirms that the approximation error is bounded given the smoothness conditions on Q-functions.

Extensive experiments conducted in diverse MARL environments like Firefighter, Adversarial Pursuit, and Battle demonstrate the efficacy of BMF, showing superior results compared to existing methods, including state-of-the-art GAT-MF. Notably, BMF exhibits robustness in dynamic settings and competitive tasks, substantively reducing both time and space costs compared to GAT-MF.

Implications and Future Directions

Practically, the BMF method provides significant advancements in scalability and adaptability for large-scale MARL applications, suggesting potential deployments in areas requiring efficient coordination among numerous agents, such as automated traffic systems, large-scale resource management, and advanced robotics.

Theoretically, BMF extends the understanding of agent interactions, introducing novel frameworks for modeling agent diversity and dynamic interactions. This approach encourages further exploration of hierarchical and adaptive grouping techniques in RL, potentially inspiring more generalizable agent-based systems.

Future research could delve into refining clustering methodologies within BMF to enhance grouping precision or integrate deep learning techniques to further capture complex agent dynamics in real-time scenarios. Additionally, exploring BMF's applicability to more diverse MARL challenges would enrich its scope and validate its utility in broader AI contexts.