针对边缘联邦学习的拓扑优化难题，提出兼顾异构性与能效的新框架。

Federated learning (FL) has emerged as a promising paradigm within edge computing (EC) systems, enabling numerous edge devices to collaboratively train artificial intelligence (AI) models while maintaining data privacy. To overcome the communication bottlenecks associated with centralized parameter servers, decentralized federated learning (DFL), which leverages peer-to-peer (P2P) communication, has been extensively explored in the research community. Although researchers design a variety of DFL approach to ensure model convergence, its iterative learning process inevitably incurs considerable cost along with the growth of model complexity and the number of participants. These costs are largely influenced by the dynamic changes of topology in each training round, particularly its sparsity and connectivity conditions. Furthermore, the inherent resources heterogeneity in the edge environments affects energy efficiency of learning process, while data heterogeneity degrades model performance. These factors pose significant challenges to the design of an effective DFL framework for EC systems. To this end, we propose Hat-DFed, a heterogeneity-aware and coset-effective decentralized federated learning (DFL) framework. In Hat-DFed, the topology construction is formulated as a dual optimization problem, which is then proven to be NP-hard, with the goal of maximizing model performance while minimizing cumulative energy consumption in complex edge environments. To solve this problem, we design a two-phase algorithm that dynamically constructs optimal communication topologies while unbiasedly estimating their impact on both model performance and energy cost. Additionally, the algorithm incorporates an importance-aware model aggregation mechanism to mitigate performance degradation caused by data heterogeneity.