Ahmed Khaled

Abdurakhmon Sadiev, Grigory Malinovsky, Eduard Gorbunov et al. · princeton

Gradient compression is a popular technique for improving communication complexity of stochastic first-order methods in distributed training of machine learning models. However, the existing works consider only with-replacement sampling of stochastic gradients. In contrast, it is well-known in practice and recently confirmed in theory that stochastic methods based on without-replacement sampling, e.g., Random Reshuffling (RR) method, perform better than ones that sample the gradients with-replacement. In this work, we close this gap in the literature and provide the first analysis of methods with gradient compression and without-replacement sampling. We first develop a naïve combination of random reshuffling with gradient compression (Q-RR). Perhaps surprisingly, but the theoretical analysis of Q-RR does not show any benefits of using RR. Our extensive numerical experiments confirm this phenomenon. This happens due to the additional compression variance. To reveal the true advantages of RR in the distributed learning with compression, we propose a new method called DIANA-RR that reduces the compression variance and has provably better convergence rates than existing counterparts with with-replacement sampling of stochastic gradients. Next, to have a better fit to Federated Learning applications, we incorporate local computation, i.e., we propose and analyze the variants of Q-RR and DIANA-RR -- Q-NASTYA and DIANA-NASTYA that use local gradient steps and different local and global stepsizes. Finally, we conducted several numerical experiments to illustrate our theoretical results.

Ahmed Khaled, Satyen Kale, Arthur Douillard et al.

Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in such settings but methods like Local Stochastic Gradient Descent (Local SGD) show great promise in reducing this additional communication overhead. Local SGD consists of three parts: a local optimization process, an aggregation mechanism, and an outer optimizer that uses the aggregated updates from the nodes to produce a new model. While there exists an extensive literature on understanding the impact of hyperparameters in the local optimization process, the choice of outer optimizer and its hyperparameters is less clear. We study the role of the outer optimizer in Local SGD, and prove new convergence guarantees for the algorithm. In particular, we show that tuning the outer learning rate allows us to (a) trade off between optimization error and stochastic gradient noise variance, and (b) make up for ill-tuning of the inner learning rate. Our theory suggests that the outer learning rate should sometimes be set to values greater than $1$. We extend our results to settings where we use momentum in the outer optimizer, and we show a similar role for the momentum-adjusted outer learning rate. We also study acceleration in the outer optimizer and show that it improves the convergence rate as a function of the number of communication rounds, improving upon the convergence rate of prior algorithms that apply acceleration locally. Finally, we also introduce a novel data-dependent analysis of Local SGD that yields further insights on outer learning rate tuning. We conduct comprehensive experiments with standard language models and various outer optimizers to validate our theory.