Hierarchical Multiagent Reinforcement Learning for Multi-Group Tax Game

Multi-agent reinforcement learning (MARL) systems face fundamental challenges in balancing global coordination with local execution across different temporal scales. This paper introduces the Coupled Hierarchical Multi-Agent System (CHMAS), a novel framework that decomposes multi-agent decision-making into centralized strategic planning and distributed tactical execution with bidirectional information flow. The strategic layer integrates all agents' states with an exclusive global environmental state to generate guidance actions every $T$ timesteps, while tactical agents execute distributed policies augmented by strategic guidance and local neighborhood observations. Unlike existing hierarchical approaches with unidirectional control, CHMAS establishes a feedback mechanism where accumulated tactical rewards influence strategic objectives through a coupling coefficient $λ$, ensuring strategic plans remain grounded in tactical feasibility. To address the non-stationarity inherent in hierarchical learning, we propose an asynchronous update protocol where strategic parameters update every $N_f$ tactical episodes, allowing tactical policies to converge to quasi-stationary points between strategic changes. We present both a general bi-level formulation capturing full system dynamics and a tractable additive approximation enabling rigorous analysis. Theoretical analysis proves that this asynchronous scheme achieves $\mathcal{O}(\log K/\sqrt{K})$ convergence for the strategic layer after $K$ strategic updates under standard assumptions. Experimental validation in a multi-agent foraging domain demonstrates successful learning of spatially partitioned exploration strategies, with both layers converging stably despite hierarchical coupling.

Decentralized Multi-Agent Reinforcement Learning (MARL) methods allow for learning scalable multi-agent policies, but suffer from partial observability and induced non-stationarity. These challenges can be addressed by introducing mechanisms that facilitate coordination and high-level planning. Specifically, coordination and temporal abstraction can be achieved through communication (e.g., message passing) and Hierarchical Reinforcement Learning (HRL) approaches to decision-making. However, optimization issues limit the applicability of hierarchical policies to multi-agent systems. As such, the combination of these approaches has not been fully explored. To fill this void, we propose a novel and effective methodology for learning multi-agent hierarchies of message-passing policies. We adopt the feudal HRL framework and rely on a hierarchical graph structure for planning and coordination among agents. Agents at lower levels in the hierarchy receive goals from the upper levels and exchange messages with neighboring agents at the same level. To learn hierarchical multi-agent policies, we design a novel reward-assignment method based on training the lower-level policies to maximize the advantage function associated with the upper levels. Results on relevant benchmarks show that our method performs favorably compared to the state of the art.

In this paper we study team-symmetric games with $m\ge 2$ teams. Players within a team have symmetric identity and have a common payoff function. We show that team-symmetric games always have a team-symmetric Nash equilibrium. We develop and solve a linear complementarity problem of team-symmetric Nash equilibria. We propose an actor-critic based multi-agent reinforcement learning algorithm for team-symmetric games. Through simulations, we show that this multi-agent reinforcement learning algorithm performs much better than many existing algorithms.