The performance of distributed ML training is largely determined by workers that generate gradients in the slowest pace, i.e., stragglers. The state-of-the-art load balancing approaches consider that each worker stores a complete dataset locally and the data fetching time can be ignored. They only consider the computation capacity of workers in equalizing the gradient computation time. However, we find that in scenarios of ML on distributed datasets, whether in edge computing or distributed data cache systems, the data fetching time is non-negligible and often becomes the primary cause of stragglers. In this paper, we present LOFT, an adaptive load balancing approach for ML upon distributed datasets at the edge. It aims to balance the time to generate gradients at each worker while ensuring the model accuracy. Specifically, LOFT features a locality-aware batching. It builds performance and optimization models upon data fetching and gradient computation time. Leveraging the models, it develops an adaptive scheme based on grid search. Furthermore, it offers Byzantine gradient aggregation upon Ring All-Reduce, which makes itself fault-tolerant under Byzantine gradients brought by a small batch size. Experiments with twelve public DNN models and four open datasets show that LOFT reduces the training time by up to 46%, while reducing the training loss by up to 67% compared to LB-BSP.