Distributed learning has gained significant attention due to its advantages in scalability, privacy, and fault tolerance.In this paradigm, multiple agents collaboratively train a global model by exchanging parameters only with their neighbors. However, a key vulnerability of existing distributed learning approaches is their implicit assumption that all agents behave honestly during gradient updates. In real-world scenarios, this assumption often breaks down, as selfish or strategic agents may be incentivized to manipulate gradients for personal gain, ultimately compromising the final learning outcome. In this work, we propose a fully distributed payment mechanism that, for the first time, guarantees both truthful behaviors and accurate convergence in distributed stochastic gradient descent. This represents a significant advancement, as it overcomes two major limitations of existing truthfulness mechanisms for collaborative learning:(1) reliance on a centralized server for payment collection, and (2) sacrificing convergence accuracy to guarantee truthfulness. In addition to characterizing the convergence rate under general convex and strongly convex conditions, we also prove that our approach guarantees the cumulative gain that an agent can obtain through strategic behavior remains finite, even as the number of iterations approaches infinity--a property unattainable by most existing truthfulness mechanisms. Our experimental results on standard machine learning tasks, evaluated on benchmark datasets, confirm the effectiveness of the proposed approach.

翻译：分布式学习因其在可扩展性、隐私性和容错性方面的优势而受到广泛关注。在该范式中，多个智能体仅通过与邻居交换参数来协作训练全局模型。然而，现有分布式学习方法的一个关键漏洞在于其隐含假设所有智能体在梯度更新过程中行为诚实。在现实场景中，这一假设往往不成立，因为自私或策略性智能体可能为了个人利益而操控梯度，最终损害最终学习结果。在本工作中，我们提出了一种全分布式支付机制，该机制首次在分布式随机梯度下降中同时保证诚实行为和精确收敛。这代表了重大进展，因为它克服了现有协作学习诚实性机制的两个主要局限：（1）依赖中心化服务器进行支付收集，以及（2）为保障诚实性而牺牲收敛精度。除了刻画一般凸和强凸条件下的收敛速率外，我们还证明该方法能确保智能体通过策略行为获得的累积收益在迭代次数趋于无穷时仍保持有限——这是多数现有诚实性机制无法实现的特性。我们在标准机器学习任务上、基于基准数据集进行的实验结果，证实了所提方法的有效性。