Byzantine-Robust Decentralized Federated Learning Federated learning (FL) enables multiple clients to collaboratively train machine learning models without revealing their private training data. In conventional FL, the system follows the server-assisted architecture, where the training process is coordinated by a central server. However, the server-assisted FL framework suffers from poor scalability due to a communication bottleneck at the server and trust dependency issues. To address these challenges, decentralized federated learning (DFL) has been proposed to allow clients to train models collaboratively in a serverless and peer-to-peer manner. However, DFL is highly vulnerable to poisoning attacks, where malicious clients could manipulate the system by sending carefully-crafted local models to their neighboring clients. To date, only a limited number of Byzantine-robust DFL methods have been proposed, most of which are either communication-inefficient or remain vulnerable to advanced poisoning attacks. In this paper, we propose a new algorithm called BALANCE (Byzantine-robust averaging through local similarity in decentralization) to defend against poisoning attacks in DFL. In BALANCE, each client leverages its own local model as a similarity reference to determine if the received model is malicious or benign. We establish the theoretical convergence guarantee for BALANCE under poisoning attacks in both strongly convex and non-convex settings. Furthermore, the convergence rate of BALANCE under poisoning attacks matches those of the state-of-the-art counterparts in Byzantine-free settings. Extensive experiments also demonstrate that BALANCE outperforms existing DFL methods and effectively defends against poisoning attacks. BALANCE is a novel approach to defend against poisoning attacks in DFL. In contrast to existing DFL defenses, our BALANCE algorithm achieves the same communication complexity as that of the state-of-the-art server-assisted FL algorithms. We theoretically establish the convergence rate performance of BALANCE under poisoning attacks in both strongly convex and non-convex settings. We note that the convergence rate performance of BALANCE under strongly convex and non-convex settings match the optimal convergence rates in Byzantine-free strongly convex and non-convex optimizations, respectively. Our extensive experiments on different benchmark datasets, various poisoning attacks and practical DFL settings demonstrate and verify the efficacy of our proposed BALANCE method.Byzantine-Robust Decentralized Federated Learning Federated learning (FL) enables multiple clients to collaboratively train machine learning models without revealing their private training data. In conventional FL, the system follows the server-assisted architecture, where the training process is coordinated by a central server. However, the server-assisted FL framework suffers from poor scalability due to a communication bottleneck at the server and trust dependency issues. To address these challenges, decentralized federated learning (DFL) has been proposed to allow clients to train models collaboratively in a serverless and peer-to-peer manner. However, DFL is highly vulnerable to poisoning attacks, where malicious clients could manipulate the system by sending carefully-crafted local models to their neighboring clients. To date, only a limited number of Byzantine-robust DFL methods have been proposed, most of which are either communication-inefficient or remain vulnerable to advanced poisoning attacks. In this paper, we propose a new algorithm called BALANCE (Byzantine-robust averaging through local similarity in decentralization) to defend against poisoning attacks in DFL. In BALANCE, each client leverages its own local model as a similarity reference to determine if the received model is malicious or benign. We establish the theoretical convergence guarantee for BALANCE under poisoning attacks in both strongly convex and non-convex settings. Furthermore, the convergence rate of BALANCE under poisoning attacks matches those of the state-of-the-art counterparts in Byzantine-free settings. Extensive experiments also demonstrate that BALANCE outperforms existing DFL methods and effectively defends against poisoning attacks. BALANCE is a novel approach to defend against poisoning attacks in DFL. In contrast to existing DFL defenses, our BALANCE algorithm achieves the same communication complexity as that of the state-of-the-art server-assisted FL algorithms. We theoretically establish the convergence rate performance of BALANCE under poisoning attacks in both strongly convex and non-convex settings. We note that the convergence rate performance of BALANCE under strongly convex and non-convex settings match the optimal convergence rates in Byzantine-free strongly convex and non-convex optimizations, respectively. Our extensive experiments on different benchmark datasets, various poisoning attacks and practical DFL settings demonstrate and verify the efficacy of our proposed BALANCE method.