论文标题
部分可观测时空混沌系统的无模型预测
ISFL: Federated Learning for Non-i.i.d. Data with Local Importance Sampling
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
As a promising learning paradigm integrating computation and communication, federated learning (FL) proceeds the local training and the periodic sharing from distributed clients. Due to the non-i.i.d. data distribution on clients, FL model suffers from the gradient diversity, poor performance, bad convergence, etc. In this work, we aim to tackle this key issue by adopting importance sampling (IS) for local training. We propose importance sampling federated learning (ISFL), an explicit framework with theoretical guarantees. Firstly, we derive the convergence theorem of ISFL to involve the effects of local importance sampling. Then, we formulate the problem of selecting optimal IS weights and obtain the theoretical solutions. We also employ a water-filling method to calculate the IS weights and develop the ISFL algorithms. The experimental results on CIFAR-10 fit the proposed theorems well and verify that ISFL reaps better performance, sampling efficiency, as well as explainability on non-i.i.d. data. To the best of our knowledge, ISFL is the first non-i.i.d. FL solution from the local sampling aspect which exhibits theoretical compatibility with neural network models. Furthermore, as a local sampling approach, ISFL can be easily migrated into other emerging FL frameworks.
