Federated Stochastic Gradient Langevin Dynamics
This addresses challenges in federated learning for non-IID data, offering a method to improve posterior sampling, though it appears incremental as an extension of existing SGLD techniques.
The paper tackled the problem of applying stochastic gradient MCMC methods like SGLD to federated non-IID data, where variance increases and delayed communication causes divergence from the true posterior, and proposed conducive gradients to correct gradient updates, showing that FSGLD converges to the target posterior where DSGLD fails and outperforms it in experiments on metric learning and neural networks.
Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.