FedAda: Fast-convergent adaptive federated learning in heterogeneous mobile edge computing environment

Abstract

With rapid advancement of Internet of Things (IoT) and social networking applications generating large amounts of data at or close to the network edge, Mobile Edge Computing (MEC) has naturally been proposed to bring model training closer to where data is produced. However, there still exists privacy concern since typical MEC frameworks need to transfer sensitive data resources from data collection end devices/clients to MEC server. So the concept of Federated Learning (FL) has been introduced which supports privacy-preserved collaborative machine learning involving multiple clients coordinated by the MEC server without centralizing the private data. Unfortunately, FL is prone to multiple challenges: 1) systems heterogeneity between clients causes straggler issue, and 2) statistical heterogeneity between clients brings about objective inconsistency problem, both of which may lead to a significant slow-down in the convergence speed in heterogeneous MEC environment. In this paper, we propose a novel framework, FedAda (Federated Adaptive Training), that incorporates systems capabilities and data characteristics of the clients to adaptively assign appropriate workload to each client. The key idea is that instead of running a fixed number of local training iterations as in Federated Averaging (FedAvg), our algorithm adopts an adaptive workload assignment strategy by minimizing the runtime gap between clients and maximizing convergence gain in heterogeneous MEC environment. Moreover, we design a light mechanism extending FedAda to accelerate the convergence speed by further fine-tuning the workload assignment based on the global convergence status in each communication round. We evaluate FedAda on CIFAR-10 dataset to explore the performance of the algorithm in the simulated heterogeneous MEC environment. Experimental results show that FedAda is able to assign appropriate amount of workload to each client and substantially reduces the convergence time by up to 49.5% compared to FedAvg in heterogeneous MEC environment. In addition, we demonstrate that fine-tuning the workload assignment can help FedAda improve the learning performance in heterogeneous mobile edge computing environment.

Appendix A: Derivation of the analytical solution of the optimization objective function

Since $f(w^*)=0$ and $\tau _i^{\prime } = \beta \tau _i$, Equation (9) can be turned into:

$$\begin{aligned} \frac{f(w^t)}{\beta \sum _{i=1}^{N}{ \tau _i}} + \lambda { { \beta ^2 \tau _{max}}^2} \end{aligned}$$

(17)

And then multiply Equation (17) by the constant $\sum _{i=1}^N\tau _i$, producing a new objective function:

$$\begin{aligned} h(\beta ) = \frac{f(w^t)}{\beta } + \lambda { { \beta ^2 \tau _{max}}^2\sum _{i=1}^{N}{ \tau _i}} \end{aligned}$$

(18)

Since at the beginning of each communication round, every $\tau _i$ is already known, so let $K={ \tau _{max}}^2\sum _{i=1}^{N}{ \tau _i}$ and the optimization objective becomes:

$$\begin{aligned} h(\beta ) = \frac{f(w^t)}{\beta } + \lambda \beta ^2K \end{aligned}$$

(19)

Take the derivative with respect to h:

$$\begin{aligned} \frac{dh}{d\beta } = -\frac{f(w^t)}{\beta ^2} + 2\lambda \beta K \end{aligned}$$

(20)

Let $\frac{dh}{d\beta } = 0$, we can get the analytical solution $\beta = \root 3 \of {\frac{f(w^t)}{2\lambda K}}$ of the optimization objective function $h(\beta )$ with respect to $\beta$. The value of $\beta$ shall decrease with the decrease of the average loss function $f(w^t)$.

At the beginning of training process, the decay value should be $\beta =1$, and the loss function value on the initial model should be $f(w^0)$. It’s easy to achieve $\beta = \root 3 \of {\frac{f(w^0)}{2\lambda K}} = 1$, so the constant $\lambda =\frac{f(w^0)}{2K}$. By substituting the constant into the analytical solution, the optimal solution of the optimization objective function in the communication round t can be obtained as Equation (16).