Optimization methods are crucial to the success of machine learning, with Stochastic Gradient Descent (SGD) serving as a foundational algorithm for training models. However, SGD is often sensitive to the choice of the learning rate, which necessitates extensive hyperparameter tuning. In this work, we introduce a new variant of SGD that brings enhanced stability in two key aspects. First, our method allows the use of the same fixed learning rate to attain optimal convergence rates regardless of the noise magnitude, eliminating the need to adjust learning rates between noiseless and noisy settings. Second, our approach achieves these optimal rates over a wide range of learning rates, significantly reducing sensitivity compared to standard SGD, which requires precise learning rate selection. Our key innovation is a novel gradient estimator based on a double-momentum mechanism that combines two recent momentum-based techniques. Utilizing this estimator, we design both standard and accelerated algorithms that are robust to the choice of learning rate. Specifically, our methods attain optimal convergence rates in both noiseless and noisy stochastic convex optimization scenarios without the need for learning rate decay or fine-tuning. We also prove that our approach maintains optimal performance across a wide spectrum of learning rates, underscoring its stability and practicality. Empirical studies further validate the robustness and enhanced stability of our approach.

In this paper, we investigate the challenging framework of Byzantine-robust training in distributed machine learning (ML) systems, focusing on enhancing both efficiency and practicality. As distributed ML systems become integral for complex ML tasks, ensuring resilience against Byzantine failures—where workers may contribute incorrect updates due to malice or error—gains paramount importance. Our first contribution is the introduction of the Centered Trimmed Meta Aggregator (CTMA), an efficient meta-aggregator that upgrades baseline aggregators to optimal performance levels, while requiring low computational demands. Additionally, we propose harnessing a recently developed gradient estimation technique based on a double-momentum strategy within the Byzantine context. Our paper highlights its theoretical and practical advantages for Byzantine-robust training, especially in simplifying the tuning process and reducing the reliance on numerous hyperparameters. The effectiveness of this technique is supported by theoretical insights within the stochastic convex optimization (SCO) framework and corroborated by empirical evidence.

We address the challenges of Byzantine-robust training in asynchronous distributed machine learning systems, aiming to enhance efficiency amid massive parallelization and heterogeneous compute resources. Asynchronous systems, marked by independently operating workers and intermittent updates, uniquely struggle with maintaining integrity against Byzantine failures, which encompass malicious or erroneous actions that disrupt learning. The inherent delays in such settings not only introduce additional bias to the system but also obscure the disruptions caused by Byzantine faults. To tackle these issues, we adapt the Byzantine framework to asynchronous dynamics by introducing a novel weighted robust aggregation framework. This allows for the extension of robust aggregators and a recent meta-aggregator to their weighted versions, mitigating the effects of delayed updates. By further incorporating a recent variance-reduction technique, we achieve an optimal convergence rate for the first time in an asynchronous Byzantine environment. Our methodology is rigorously validated through empirical and theoretical analysis, demonstrating its effectiveness in enhancing fault tolerance and optimizing performance in asynchronous ML systems.

We consider distributed learning scenarios where $M$ machines interact with a parameter server along several communication rounds in order to minimize a joint objective function. Focusing on the heterogeneous case, where different machines may draw samples from different data-distributions, we design the first local update method that provably benefits over the two most prominent distributed baselines: namely Minibatch-SGD and Local-SGD. Key to our approach is a slow querying technique that we customize to the distributed setting, which in turn enables a better mitigation of the bias caused by local updates.