In this paper, we perform a non-asymptotic analysis of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the bias introduced by local training with heterogeneous agents, and investigate the sample complexity of the algorithm. We show that the communication complexity of FedLSA scales polynomially with the desired precision $\epsilon$, which limits the benefits of federation. To overcome this, we propose SCAFFLSA, a novel variant of FedLSA, that uses control variates to correct the bias of local training, and prove its convergence without assumptions on statistical heterogeneity. We apply the proposed methodology to federated temporal difference learning with linear function approximation, and analyze the corresponding complexity improvements.

翻译：本文对联邦线性随机逼近（FedLSA）算法进行了非渐近分析。我们明确量化了异质性主体进行本地训练所引入的偏差，并研究了该算法的样本复杂度。研究表明，FedLSA的通信复杂度随期望精度$\epsilon$呈多项式增长，这限制了联邦学习的优势。为解决此问题，我们提出SCAFFLSA——一种FedLSA的新型变体，通过使用控制变量矫正本地训练的偏差，并在无需统计异质性假设的条件下证明了其收敛性。我们将所提方法应用于基于线性函数逼近的联邦时间差分学习，并分析了相应的复杂度改进。