Federated learning (FL) with differential privacy (DP) provides a framework for collaborative machine learning, enabling clients to train a shared model while adhering to strict privacy constraints. The framework allows each client to have an individual privacy guarantee, e.g., by adding different amounts of noise to each client's model updates. One underlying assumption is that all clients spend their privacy budgets uniformly over time (learning rounds). However, it has been shown in the literature that learning in early rounds typically focuses on more coarse-grained features that can be learned at lower signal-to-noise ratios while later rounds learn fine-grained features that benefit from higher signal-to-noise ratios. Building on this intuition, we propose a time-adaptive DP-FL framework that expends the privacy budget non-uniformly across both time and clients. Our framework enables each client to save privacy budget in early rounds so as to be able to spend more in later rounds when additional accuracy is beneficial in learning more fine-grained features. We theoretically prove utility improvements in the case that clients with stricter privacy budgets spend budgets unevenly across rounds, compared to clients with more relaxed budgets, who have sufficient budgets to distribute their spend more evenly. Our practical experiments on standard benchmark datasets support our theoretical results and show that, in practice, our algorithms improve the privacy-utility trade-offs compared to baseline schemes.

In this paper, we focus on approaches to parallelizing stochastic gradient descent (SGD) wherein data is farmed out to a set of workers, the results of which, after a number of updates, are then combined at a central master node. Although such synchronized SGD approaches parallelize well in idealized computing environments, they often fail to realize their promised computational acceleration in practical settings. One cause is slow workers, termed stragglers, who can cause the fusion step at the master node to stall, which greatly slowing convergence. In many straggler mitigation approaches work completed by these nodes, while only partial, is discarded completely. In this paper, we propose an approach to parallelizing synchronous SGD that exploits the work completed by all workers. The central idea is to fix the computation time of each worker and then to combine distinct contributions of all workers. We provide a convergence analysis and optimize the combination function. Our numerical results demonstrate an improvement of several factors of magnitude in comparison to existing methods.